The Mathematics of Maybe: Introduction to Probability (Shayad ka Ganit: Probability ka Introduction): Class 9 Maths Chapter 7 Hinglish mein

1. 1
   Short answerEasyNCERT Exercise Set 7.1, Q1

   Har event ko probability scale par rakho: impossible, less likely, even chance, more likely ya certain chuno. Phir reason bhi do.

   AI se poochho

   1. (a)

      Calendar se random chuna gaya mahina kam se kam 28 din ka hai.

      AimpossibleBless likelyCeven chanceDmore likelyEcertain

      Check karo

      Answer dekho

      Answer (E) certain

      February mein bhi 28 din hote hain, isliye har mahina is shart par khara utarta hai: event certain hai, probability 1.

      Hint

      Kya yeh ho bhi sakta hai? Kya yeh hona hi hai? Agar dono nahi, to ise coin ke heads aane se compare karo.

   2. (b)

      Agle birthday par tumhari umar aaj ki umar se kam hogi.

      AimpossibleBless likelyCeven chanceDmore likelyEcertain

      Check karo

      Answer dekho

      Answer (A) impossible

      Umar sirf badhti hai, isliye yeh ho hi nahi sakta: probability 0.
   3. (c)

      Ek baar toss kiya gaya fair coin heads par girta hai.

      AimpossibleBless likelyCeven chanceDmore likelyEcertain

      Check karo

      Answer dekho

      Answer (C) even chance

      Heads aur tails equally likely hain, isliye probability 0.5 hai.
   4. (d)

      52 cards ke poore pack se nikala gaya card spade nahi hai.

      AimpossibleBless likelyCeven chanceDmore likelyEcertain

      Check karo

      Answer dekho

      Answer (D) more likely

      52 mein se 39 cards spades nahi hain, isliye probability $\frac{39}{52}=0.75$ hai: hone ki sambhavna zyada hai, lekin certain nahi.
   5. (e)

      Ek baar roll kiya gaya die 6 dikhata hai.

      AimpossibleBless likelyCeven chanceDmore likelyEcertain

      Check karo

      Answer dekho

      Answer (B) less likely

      Chhe faces mein se sirf ek par 6 hai, isliye chance $\frac{1}{6}$ hai, jo 0.5 se kaafi neeche hai.

1. 1
   NumericalEasyNCERT Exercise Set 7.2, Q1

   Ek chudi bechne wala ek bade box se 40 chudiyon ka sample leta hai: 13 maroon, 12 pink, 9 golden aur 6 silver.

   AI se poochho

   1. (a)

      Sample se random chuni gayi chudi ke golden hone ki probability ka estimate lagao.

      Check karo

      Answer dekho

      Answer 0.225

      $\frac{9}{40}=0.225$.

      Hint

      Golden chudiyan ÷ sample ki saari chudiyan.

   2. (b)

      Box mein 1000 chudiyan hain. Estimate lagao ki unmein se kitni silver hain.

      Check karo

      Answer dekho

      Answer 150

      $\frac{6}{40}=0.15$, aur $0.15\times 1000=150$ silver chudiyan.
2. 2
   NumericalMediumNCERT Exercise Set 7.2, Q2

   1200 students wale school se random chune gaye pachaas students se poochha gaya ki woh aam taur par school kaise aate hain. Unke jawab: paidal 18, school bus 15, bicycle 12, car ya scooter 5.

   AI se poochho

   1. (a)

      Sample ke kisi student ke cycle se school aane ki probability ka estimate lagao.

      Check karo

      Answer dekho

      Answer 0.24

      $\frac{12}{50}=0.24$.
   2. (b)

      School ke 1200 students mein se lagbhag kitne school bus se aate hain?

      Check karo

      Answer dekho

      Answer 360

      $\frac{15}{50}=0.3$, aur $0.3\times 1200=360$ students.

      Hint

      Bus ke liye sample fraction nikaalo, phir use 1200 tak scale up karo.

3. 3
   ActivityEasyNCERT Exercise Set 7.2, Q3

   Ek die 30 baar roll karo aur har result record karo.

   AI se poochho

   1. (a)

      Tumhe kitni baar 5 mila?

      Solution dikhao

      Yeh tumhare apne rolls par depend karta hai. Lagbhag 2 se 8 tak ke counts aam hain. Sabse typical lagbhag 5 hai, kyunki $30\times \frac{1}{6}=5$.

   2. (b)

      5 roll karne ki apni experimental probability nikaalo.

      Solution dikhao

      Apne count ko 30 se divide karo. Jaise, 4 fives se $\frac{4}{30}\approx 0.133$ milta hai.

   3. (c)

      Tumhare agle roll par 5 aane ki probability kya hai?

      Check karo

      Answer dekho

      Answer 0.1667

      Har roll pichhle rolls se independent hai, isliye $P(5)=\frac{1}{6}\approx 0.167$, chahe tumhare 30 rolls mein kuch bhi hua ho.

      Hint

      Kya die ko tumhare pichhle rolls yaad rehte hain?

4. 4
   ActivityMediumNCERT Exercise Set 7.2, Q4

   Ek khaali matchbox 50 baar toss karo. Har baar record karo ki woh badi face par gira, lambi side par ya chhote end par.

   AI se poochho

   1. (a)

      Apne results se girne ke har tareeke ki experimental probability batao.

      Solution dikhao

      Har count ko 50 se divide karo. Ek class ko badi face 38, lambi side 10 aur chhota end 2 mila, jisse 0.76, 0.2 aur 0.04 aaye. Tumhare numbers alag honge, lekin unka total 1 hona chahiye.

   2. (b)

      Kya girne ke har tareeke ki probability $\frac{1}{3}$ honi chahiye? Samjhao.

      Hint

      Kya matchbox die ki tarah symmetric hai?

      Solution dikhao

      Nahi. Teeno outcomes equally likely nahi hain: badi face ek chaudi, tiki hui base hai, jabki chhota end patla aur dagmagata hai. Aisi cheezon ke liye sirf experiment hi hamein probabilities bata sakta hai.

5. 5
   Quick answerEasyNCERT Exercise Set 7.2, Q5

   Tum ek fair die ek baar roll karte ho. Prime number aane ki kitni sambhavna hai? Probability chuno.

   A$\frac{1}{3}$B$\frac{1}{2}$C$\frac{2}{3}$D$\frac{1}{6}$

   Check karo

   Answer dekho

   Answer (B) $\frac{1}{2}$

   Die par primes 2, 3 aur 5 hain (1 prime nahi hai), isliye $P=\frac{3}{6}=\frac{1}{2}$.

   HintAI se poochho

   Kya 1 prime number hai?

6. 6
   NumericalMediumNCERT Exercise Set 7.2, Q6

   Ek fair spinner ke chaar barabar sectors hain jin par A, B, C aur D likha hai. Ravi ise 16 baar ghumata hai, aur yeh 7 baar C par rukta hai.

   AI se poochho

   1. (a)

      C ki experimental probability kya hai?

      Check karo

      Answer dekho

      Answer 0.4375

      $\frac{7}{16}=0.4375$.
   2. (b)

      C ki theoretical probability kya hai?

      Check karo

      Answer dekho

      Answer 0.25

      Chaar equally likely sectors mein se ek favourable sector: $\frac{1}{4}=0.25$.
   3. (c)

      Dono answers alag kyun hain? 40, 400 aur 4000 spins ke baad tum kya expect karoge?

      Hint

      Law of large numbers ke baare mein socho.

      Solution dikhao

      Solah spins kam trials hain, isliye chance aasaani se C ko uske fair hisse se upar dhakel sakta hai. 40 spins par bhi fraction 0.25 se thoda door ho sakta hai. 400 aur phir 4000 spins ke baad yeh 0.25 ke aur paas, aur paas tikna chahiye, jaisa law of large numbers kehta hai.

1. 1
   Quick answerEasyNCERT Exercise Set 7.3, Q1

   Ek spinner ke 1 se 9 tak number wale nau barabar sectors hain. Ek spin ke sample space mein kitne outcomes hain?

   Check karo

   Answer dekho

   Answer 9

   Har sector ka ek outcome hai, isliye $n(S)=9$.

   HintAI se poochho

   Har sector ke liye ek outcome.

2. 2
   Short answerMediumNCERT Exercise Set 7.3, Q2

   Har experiment ka sample space likho.

   AI se poochho

   1. (a)

      Red, green aur blue sectors wala spinner ghumaaya jaata hai aur ek coin toss kiya jaata hai.

      Hint

      Har colour ko coin ke har face ke saath jodo.

      Solution dikhao

      Har colour ko har face ke saath jodo: $S=\{RH,RT,GH,GT,BH,BT\}$, isliye $n(S)=6$.

   2. (b)

      $-3\le x\le 3$ wala ek integer $x$ random chuna jaata hai.

      Solution dikhao

      $S=\{-3,-2,-1,0,1,2,3\}$. 0 ko shaamil karna mat bhoolo, jisse $n(S)=7$ milta hai.

   3. (c)

      Ek bag mein 4 white aur 6 black counters hain, aur ek counter nikaala jaata hai.

      Solution dikhao

      Agar hum sirf colour record karein, to $S=\{\text{white},\text{black}\}$, lekin yeh do outcomes equally likely nahi hain. Ginti use karne ke liye counters ko $W_1,\dots ,W_4$ aur $B_1,\dots ,B_6$ label karo. Tab $S$ mein 10 equally likely elements hain.

3. 3
   Short answerEasyNCERT Exercise Set 7.3, Q3

   School fete mein tum ek mithai (jalebi ya rasgulla) aur ek drink (nimbu pani, chaas ya coconut water) chunte ho.

   AI se poochho

   1. (a)

      Mithai-aur-drink ke saare choices ka sample space list karo.

      Hint

      Ek table banao jismein mithaiyan rows hon aur drinks columns.

      Solution dikhao

      Jalebi ke liye J, rasgulla ke liye R aur drinks ke liye N, C, W likho. Tab $S=\{JN,JC,JW,RN,RC,RW\}$: 6 combinations.

   2. (b)

      Event “drink chaas hai” list karo.

      Solution dikhao

      $\{JC,RC\}$: 6 combinations mein se 2.

1. 1
   DiagramMediumNCERT Exercise Set 7.4, Q1

   Tiffin box A mein 3 idlis aur 1 vada hai. Tiffin box B mein 1 laddoo, 1 barfi aur 1 peda hai. Bina dekhe tum har box se ek item nikaalte ho.

   AI se poochho

   1. (a)

      Dono picks ke liye tree diagram banao.

      Hint

      Teeno idlis ko alag-alag items maano.

      Solution dikhao

      Pehla stage (box A): chaar branches, idli 1, idli 2, idli 3 aur vada. Har ek se box B ke liye teen branches: laddoo, barfi aur peda. Isse $4\times 3=12$ paths bante hain.

   2. (b)

      Sample space list karo.

      Solution dikhao

      $I_1$, $I_2$, $I_3$, $V$ aur $L$, $B$, $P$ use karke: $S=\{I_{1}L,I_{1}B,I_{1}P,I_{2}L,I_{2}B,I_{2}P,I_{3}L,I_{3}B,I_{3}P,VL,VB,VP\}$, isliye $n(S)=12$.

   3. (c)

      Ek idli aur ek peda milne ki probability kya hai?

      Check karo

      Answer dekho

      Answer 0.25

      Favourable paths $I_{1}P$, $I_{2}P$ aur $I_{3}P$ hain, isliye $P=\frac{3}{12}=\frac{1}{4}=0.25$.
2. 2
   DiagramHardNCERT Exercise Set 7.4, Q2

   Ek jar mein 2 blue, 3 yellow aur 5 white marbles hain. Tum bina dekhe ek marble nikaalte ho, uska colour note karte ho aur use wapas jar mein daal dete ho. Phir tumhara dost bhi isi tarah apni baari leta hai.

   AI se poochho

   1. (a)

      Colours ke possible pairs dikhane wala tree diagram banao.

      Solution dikhao

      Pehla stage: blue, yellow ya white. Har ek se tumhare dost ke liye wahi teen branches, jisse BB se WW tak 9 colour pairs milte hain. Kyunki marble wapas jaata hai, dono picks ke liye jar same rehta hai.

   2. (b)

      Probability nikaalo ki tum dono same colour nikaalte ho.

      Check karo

      Answer dekho

      Answer 0.38

      Marbles ke $10\times 10=100$ equally likely ordered pairs hain. Same colour: $2\times 2+3\times 3+5\times 5=4+9+25=38$ pairs, isliye $P=\frac{38}{100}=0.38$.

      Hint

      Saare 10 marbles ko label karo taaki pairs equally likely hon, ya har branch ke saath multiply karo.

Questions 1 se 16 wahi skills practise karate hain jo NCERT ki end-of-chapter exercises mein hain, naye numbers aur situations ke saath. Questions 9 se 16 thode zyada challenging hain. Questions 17 se 19 jaldi wale extra checks hain.

1. 1
   Short answerEasyNCERT End-of-chapter Exercises, Q1

   Khaali jagah bharo.

   AI se poochho

   1. (a)

      Jo event hona pakka hai, uski probability hoti hai.

      Check karo

      Answer dekho

      Answer 1

      Certain events scale ke sabse upar hote hain: probability 1.

      Hint

      Probability scale par certain events kahan hote hain?

   2. (b)

      Random experiment ke har ek possible result ko kehte hain.

      Check karo

      Answer dekho

      Answer outcome

      Ek possible result outcome hai; sab milkar sample space banate hain.
   3. (c)

      Ek ordinary die se 7 roll karne ki probability hai.

      Check karo

      Answer dekho

      Answer 0

      Kisi face par 7 nahi hai, isliye event impossible hai: probability 0.
   4. (d)

      Ek fair spinner ke 5 barabar sectors hain, jinmein se ek red hai. Uske red par rukne ki probability hai.

      Check karo

      Answer dekho

      Answer 1/5

      Paanch mein se ek favourable sector: $\frac{1}{5}=0.2$.
2. 2
   Short answerEasyNCERT End-of-chapter Exercises, Q2

   Ek bus stop par 80 logon se poochha gaya ki kya woh roz chai peete hain, aur 28 ne haan kaha.

   AI se poochho

   1. (a)

      Number 28 “roz chai peeta hai” ki hai, aur $\frac{28}{80}$ uski hai.

      frequencyrelative frequencysample spaceevent

      Check karo

      Answer dekho

      Answer (1) frequency, (2) relative frequency

      Frequency ek count hai. Relative frequency count ko observations ki total sankhya se divide karti hai.

      Hint

      Ek count hai; doosra count ko total se divide karke milta hai.

   2. (b)

      Relative frequency ko decimal mein likho.

      Check karo

      Answer dekho

      Answer 0.35

      $\frac{28}{80}=0.35$.
3. 3
   Quick answerMediumNCERT End-of-chapter Exercises, Q3

   Inmein se kin experiments ke outcomes equally likely hain? Jitne sahi hain, sab chuno.

   AEk drawing pin giraaya jaata hai: woh point upar ya point neeche girta hai.B5 barabar sectors wala spinner ghumaaya jaata hai: woh 1, 2, 3, 4 ya 5 par rukta hai.C6 red aur 2 white balls wale bag se ek ball nikaali jaati hai: woh red hai ya white.DAchhe se shuffle kiye 52 cards ke pack se ek card nikaala jaata hai: woh red hai ya black.EEk student exam deti hai: woh pass hoti hai ya fail.

   Check karoSaare sahi options chuno

   Answer dekho

   Answer

   • (B) 5 barabar sectors wala spinner ghumaaya jaata hai: woh 1, 2, 3, 4 ya 5 par rukta hai.
   • (D) Achhe se shuffle kiye 52 cards ke pack se ek card nikaala jaata hai: woh red hai ya black.

   Spinner ke sectors barabar hain, aur pack mein 26 red aur 26 black cards hain. Drawing pin symmetric nahi hai, bag mein white se teen guna red balls hain, aur pass hona taiyaari par depend karta hai, symmetry par nahi.

   HintAI se poochho

   Symmetry dhoondho, ya har tarah ki barabar sankhya.

4. 4
   NumericalMediumNCERT End-of-chapter Exercises, Q4

   Sample space likho, phir har probability decimal mein nikaalo.

   AI se poochho

   1. (a)

      Do coins toss kiye jaate hain. Dono par same face aane ki probability nikaalo.

      Check karo

      Answer dekho

      Answer 0.5

      $S=\{HH,HT,TH,TT\}$. Same face $=\{HH,TT\}$, isliye $P=\frac{2}{4}=0.5$.
   2. (b)

      1 se 20 tak number wale bees cards shuffle karke ek nikaala jaata hai. 3 ke multiple ki probability nikaalo.

      Check karo

      Answer dekho

      Answer 0.3

      $S=\{1,2,\dots ,20\}$. 3 ke multiples 3, 6, 9, 12, 15 aur 18 hain, kul chhe, isliye $P=\frac{6}{20}=0.3$.
   3. (c)

      Die ek baar roll karo. 3 se chhota number aane ka chance nikaalo.

      Check karo

      Answer dekho

      Answer 0.3333

      $S=\{1,2,3,4,5,6\}$ aur event $\{1,2\}$ hai, isliye $P=\frac{2}{6}=\frac{1}{3}\approx 0.333$.
   4. (d)

      Ek bag mein 4 yellow, 3 green aur 5 purple balls hain, aur random ek nikaali jaati hai. Probability nikaalo ki woh green nahi hai.

      Check karo

      Answer dekho

      Answer 0.75

      12 balls hain, aur unmein se 9 green nahi hain: $\frac{9}{12}=0.75$.
   5. (e)

      Teen coins ek saath toss kiye jaate hain. Theek ek head ki probability nikaalo.

      Check karo

      Answer dekho

      Answer 0.375

      $S$ mein 8 outcomes hain, aur theek ek head $=\{HTT,THT,TTH\}$, isliye $P=\frac{3}{8}=0.375$.

      Hint

      Teen-toss wala tree use karo.

5. 5
   Quick answerEasyNCERT End-of-chapter Exercises, Q5

   Ek pencil box mein chaar pens hain jo chhoone mein ek jaise lagte hain: ek red, ek blue, ek green aur ek black. Bina dekhe ek pen nikaala jaata hai. Uske green hone ki probability kya hai? Decimal mein batao.

   Check karo

   Answer dekho

   Answer 0.25

   Chaar equally likely pens mein se ek favourable pen: $\frac{1}{4}=0.25$.

   HintAI se poochho

   Kitne pens hain, aur kitne green hain?

6. 6
   Short answerEasyNCERT End-of-chapter Exercises, Q6

   Aarav ke paas 3 kurtas (white, yellow aur green) aur 2 pyjamas (white aur black) hain.

   AI se poochho

   1. (a)

      Ek kurta aur ek pyjama ka har outfit table mein dikhao. Kitne outfits hain?

      Check karo

      Hint

      Kurtas rows mein, pyjamas columns mein.

      Solution dikhao

      Kurta	white pyjama ke saath	black pyjama ke saath
      white	white–white	white–black
      yellow	yellow–white	yellow–black
      green	green–white	green–black

   2. (b)

      Woh random ek kurta aur ek pyjama chunta hai. Dono ke white hone ki probability kya hai?

      Check karo

      Answer dekho

      Answer 0.1667

      6 equally likely outfits mein se sirf ek white–white hai: $\frac{1}{6}\approx 0.167$.
7. 7
   NumericalMediumNCERT End-of-chapter Exercises, Q7

   Ek company ne 800 LED bulbs test kiye aur record kiya ki har bulb kitne ghante chala.

   Kitne ghante chala	5000 se kam	5000 se 9999	10 000 se 14 999	15 000 ya zyada
   Bulbs ki sankhya	36	164	280	320

   AI se poochho

   1. (a)

      Bulb ke 5000 ghante se kam chalne ki probability ka estimate lagao.

      Check karo

      Answer dekho

      Answer 0.045

      $\frac{36}{800}=0.045$.

      Hint

      Check karo ki counts ka total 800 hai, phir divide karo.

   2. (b)

      Bulb ke 5000 se 14 999 ghante tak chalne ki probability ka estimate lagao.

      Check karo

      Answer dekho

      Answer 0.555

      $\frac{164+280}{800}=\frac{444}{800}=0.555$.
   3. (c)

      Bulb ke 15 000 ghante ya zyada chalne ki probability ka estimate lagao.

      Check karo

      Answer dekho

      Answer 0.4

      $\frac{320}{800}=0.4$.
8. 8
   NumericalEasyNCERT End-of-chapter Exercises, Q8

   NAGALAND ke letters 8 ek jaise cards par likhe hain, aur bina dekhe ek card nikaala jaata hai.

   AI se poochho

   1. (a)

      Probability nikaalo ki us par N ya G hai.

      Check karo

      Answer dekho

      Answer 0.375

      N do baar aur G ek baar aata hai: 8 mein se 3 cards, isliye $\frac{3}{8}=0.375$.

      Hint

      Gino ki har letter kitne cards par hai.

   2. (b)

      Probability nikaalo ki woh A nahi hai.

      Check karo

      Answer dekho

      Answer 0.625

      A 3 baar aata hai, isliye 5 cards A nahi hain: $\frac{5}{8}=0.625$.
9. 9
   NumericalMediumNCERT End-of-chapter Exercises, Q9

   Ek spinner ke 1 se 10 tak number wale 10 barabar sectors hain, sab equally likely. Decimal mein probability nikaalo ki pointer rukta hai:

   AI se poochho

   1. (a)

      number 7 par

      Check karo

      Answer dekho

      Answer 0.1

      Das mein se ek sector: $0.1$.
   2. (b)

      kisi prime number par

      Check karo

      Answer dekho

      Answer 0.4

      2, 3, 5 aur 7 prime hain (1 nahi): chaar sectors, isliye $\frac{4}{10}=0.4$.

      Hint

      Kya 1 prime number hai? Kya 9 hai?

   3. (c)

      7 se bade number par

      Check karo

      Answer dekho

      Answer 0.3

      8, 9 aur 10: teen sectors, isliye $0.3$.

      Hint

      Kya 7 khud 7 se bada hai?

   4. (d)

      11 se chhote number par

      Check karo

      Answer dekho

      Answer 1

      Har sector ka number 11 se chhota hai, isliye yeh certain hai: probability 1.
   5. (e)

      4 ke multiple par

      Check karo

      Answer dekho

      Answer 0.2

      4 aur 8: do sectors, isliye $\frac{2}{10}=0.2$.
10. 10
    DiagramHardNCERT End-of-chapter Exercises, Q10

    Ek pencil box mein 3 blue pens aur 5 black pens hain. Tum bina dekhe ek pen nikaalkar alag rakh dete ho, phir doosra pen nikaalte ho.

    AI se poochho

    1. (a)

       Har branch par probability ke saath tree diagram banao.

       Hint

       Pehli pick ke baad sirf 7 pens bache hain.

       Solution dikhao

       Pehli pick: blue $\frac{3}{8}$, black $\frac{5}{8}$. Blue pen ke baad: blue $\frac{2}{7}$, black $\frac{5}{7}$. Black pen ke baad: blue $\frac{3}{7}$, black $\frac{4}{7}$.

    2. (b)

       Pehle blue pen aur phir black pen aane ki probability nikaalo.

       Check karo

       Answer dekho

       Answer 0.2679

       Path ke saath multiply karo: $\frac{3}{8}\times \frac{5}{7}=\frac{15}{56}\approx 0.268$.
    3. (c)

       Dono pens ke black hone ki probability nikaalo.

       Check karo

       Answer dekho

       Answer 0.3571

       $\frac{5}{8}\times \frac{4}{7}=\frac{20}{56}=\frac{5}{14}\approx 0.357$.
11. 11
    Short answerMediumNCERT End-of-chapter Exercises, Q11

    Do dice roll kiye jaate hain aur dono numbers ka product note kiya jaata hai. Ek event likho jiski probability 0 ho aur ek jiski probability 1 ho.

    HintAI se poochho

    Sabse bada possible product kya hai? Kya 6 se bada koi prime product ho sakta hai?

    Solution dikhao

    AnswerJaise, “product 7 hai” (probability 0) aur “product zyada se zyada 36 hai” (probability 1).

    Probability 0: “product 7 hai”. Kyunki 7 prime hai aur 6 se bada hai, ise 1 se 6 tak ke do numbers multiply karke nahi banaya ja sakta. Probability 1: “product zyada se zyada 36 hai”, kyunki sabse bada product $6\times 6=36$ hai.

12. 12
    NumericalHardNCERT End-of-chapter Exercises, Q12

    Sample space likho, phir har probability nikaalo. Decimals mein batao.

    AI se poochho

    1. (a)

       Do dice roll kiye jaate hain. Sum ke perfect square hone ki probability nikaalo.

       Check karo

       Answer dekho

       Answer 0.1944

       Square sums 4 aur 9 hain. Sum 4: (1, 3), (2, 2), (3, 1). Sum 9: (3, 6), (4, 5), (5, 4), (6, 3). Yaani 36 mein se 7 outcomes: $\frac{7}{36}\approx 0.194$.

       Hint

       2 aur 12 ke beech kaunse perfect squares hain?

    2. (b)

       Ek bag mein 3 red, 2 green aur 1 blue ball hai. Bina replacement ke ek ke baad ek do balls nikaali jaati hain. Dono ke same colour hone ki probability nikaalo.

       Check karo

       Answer dekho

       Answer 0.2667

       $6\times 5=30$ ordered pairs hain. Same colour: red–red $3\times 2=6$, green–green $2\times 1=2$, blue–blue 0. To $P=\frac{8}{30}=\frac{4}{15}\approx 0.267$.
    3. (c)

       Teen coins toss kiye jaate hain. Probability nikaalo ki teesra coin tails dikhaye aur kul milakar theek ek head ho.

       Check karo

       Answer dekho

       Answer 0.25

       Outcomes $HTT$ aur $THT$ hain: 8 mein se 2, isliye $\frac{2}{8}=0.25$.
    4. (d)

       Digits 2, 5 aur 7 se, har digit ek baar use karke, ek three-digit number banaya jaata hai. Uske 5 se divisible hone ki probability nikaalo.

       Check karo

       Answer dekho

       Answer 0.3333

       $3\times 2\times 1=6$ numbers hain: 257, 275, 527, 572, 725 aur 752. 5 se divisible matlab end mein 5: 275 aur 725. To $P=\frac{2}{6}=\frac{1}{3}\approx 0.333$.
    5. (e)

       Ek quiz mein 2 questions hain, har ek ke 3 options aur theek ek sahi option. Ek student dono ka guess karta hai. Theek ek sahi answer ki probability nikaalo.

       Check karo

       Answer dekho

       Answer 0.4444

       Har question ka answer sahi (1 tareeka) ya galat (2 tareeke) ho sakta hai, isliye $3\times 3=9$ equally likely answer pairs hain. Theek ek sahi: sahi-phir-galat $1\times 2=2$ aur galat-phir-sahi $2\times 1=2$. To $P=\frac{4}{9}\approx 0.444$.
13. 13
    DiagramMediumNCERT End-of-chapter Exercises, Q13

    Ek bag mein A, B aur C likhi teen chits hain. Har case mein tree diagram se sample space likho.

    AI se poochho

    1. (a)

       Ek chit nikaali jaati hai, note ki jaati hai aur wapas rakh di jaati hai. Phir doosri chit nikaali jaati hai.

       Solution dikhao

       Har stage ki 3 branches hain: $S=\{AA,AB,AC,BA,BB,BC,CA,CB,CC\}$.

    2. (b)

       Ek chit nikaalkar bahar rakh li jaati hai. Phir doosri chit nikaali jaati hai.

       Hint

       Doosri baar nikaalne ke liye kitni chits bachi hain?

       Solution dikhao

       Doosre stage mein sirf bachi hui 2 chits hain: $S=\{AB,AC,BA,BC,CA,CB\}$.

    3. (c)

       Replacement ke saath $n(S)=$ . Bina replacement ke $n(S)=$ .

       Check karo

       Answer dekho

       Answer (1) 9, (2) 6

       Replacement ke saath $3\times 3=9$ aur bina replacement ke $3\times 2=6$.
14. 14
    Short answerEasyNCERT End-of-chapter Exercises, Q14

    Ek die roll kiya jaata hai aur X aur Y likhi do chits wale box se ek chit nikaali jaati hai. Sample space ke elements list karo.

    HintAI se poochho

    Die ke har face ko har chit ke saath jodo.

    Solution dikhao

    Answer12 elements, 1X se 6Y tak.

    $S=\{1X,1Y,2X,2Y,3X,3Y,4X,4Y,5X,5Y,6X,6Y\}$, isliye $n(S)=6\times 2=12$.

15. 15
    Short answerMediumNCERT End-of-chapter Exercises, Q15

    Do dice roll kiye jaate hain aur hum ginte hain ki unmein se kitne six dikhate hain. Neeche ki lists mein se sahi sample space chuno, aur samjhao ki baaki har list mein kya galat hai.

    A$\{1,2\}$B$\{0,1,2\}$C$\{0,1,2,3\}$D$\{0,1\}$

    Check karo

    HintAI se poochho

    Sixes ki sabse chhoti possible sankhya kya hai? Sabse badi?

    Solution dikhao

    $S=\{0,1,2\}$. List $\{1,2\}$ mein koi six na aane wala case chhoot gaya hai, aur $\{0,1\}$ mein double six chhoot gaya hai. List $\{0,1,2,3\}$ mein 3 hai, jo sirf do dice ke saath impossible hai.

16. 16
    NumericalHardNCERT End-of-chapter Exercises, Q16

    40 cm side wale ek square board ke beech mein 10 cm radius ka circle paint hai. Board par kisi random point par baarish ki ek boond girti hai. Uske circle ke andar girne ki probability kya hai? Decimal mein batao.

    Check karo

    HintAI se poochho

    Areas compare karo, jaise chawal ke daanon wali activity mein kiya tha.

    Solution dikhao

    $$P=\frac{\pi \times {10}^2}{40\times 40}=\frac{100\pi }{1600}=\frac{\pi }{16}\approx 0.196$$

    Board ka har point equally likely hai, isliye probability board ke area ka woh fraction hai jo circle cover karta hai.

17. 17
    Quick answerEasy

    Inmein se kaunsa kisi event ki probability nahi ho sakta?

    A0B$\frac{7}{8}$C1.25D0.001

    Check karo

    Answer dekho

    Answer (C) 1.25

    Probabilities 0 aur 1 ke beech hoti hain, isliye 1.25 bahut bada hai. 0.001 bhi, chahe bahut chhota ho, allowed hai.

    HintAI se poochho

    Probability scale kahan se shuru hota hai aur kahan khatam?

18. 18
    Quick answerMedium

    Fair die ke ek roll ke liye in events ko sabse kam likely se sabse zyada likely ke order mein rakho.

    1. 1ek even number
    2. 210 se chhota number
    3. 31 se bada number
    4. 4ek 6
    5. 5ek 7

    Check karo

    Answer dekho

    Answer

    1. ek 7
    2. ek 6
    3. ek even number
    4. 1 se bada number
    5. 10 se chhota number

    Inki probabilities 0, $\frac{1}{6}$, $\frac{1}{2}$, $\frac{5}{6}$ aur 1 hain.

    HintAI se poochho

    Har event ke favourable faces gino.

19. 19
    Quick answerEasy

    Har experiment ko uske sample space ke size se match karo.

    Left mein koi item tap karo, phir right mein uska match.

    • 1ek die
    • 2do coins
    • 3teen coins
    • 4do dice

    • 8
    • 4
    • 6
    • 36

    Check karo

    Answer dekho

    Answer

    • ek die →: 6
    • do coins →: 4
    • teen coins →: 8
    • do dice →: 36

    Har stage ke outcomes ki sankhya multiply karo: $6$, $2\times 2$, $2\times 2\times 2$ aur $6\times 6$.

    HintAI se poochho

    Har stage ke outcomes ki sankhya multiply karo.