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Infinite Turns in games (in Hindi)
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Probabilities for a fair or unfair games when game played infinitely many times until desired outcome is observed and how to simplify for sum when more than 2 dice are given

## Jagat Chaudhary is teaching live on Unacademy Plus

Jagat Chaudhary
Cofounder of Aspiration School 🏫 Qualified IIT-JEE,IIT-JAM. Expert faculty for IIT-JEE Mathematics Courses. Studied in IIT Bhubaneswar.

U
।जब।ob।ऑव।ओ
a year ago
mai samjha nhi
sir what is the solution of previous lecture assignment
plz give a hint to solve the assignment
how to solve it ?
Jagat Chaudhary
10 months ago
Bhavika, try this once. If you get wrong answer , i will tell you the solution. But if you are not getting that question, please let me know. I will help you in either sitations
Rahul Kumar
6 months ago
plz help me sir
1. IIT-JEE (main +Advanced) Probability On

2. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game.

3. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game,

4. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A)-1 6

5. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A) 51

6. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A)= 1 + 5.5.5.4 5.5.5.5.5.5.1 66 6 66

7. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A)= 1 + 5.5.5.4 5.5.5.5.5.5.1 66 6 66

8. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A)=6+5.5.5.1 +5.5.5.5.5.5.6+-. which in infinte GP

9. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A)=6+5.5.5.1 +5.5.5.5.5.5.6+-. which in infinte GP 36 91

10. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Bail from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, P(A)=6+5.5.5.1 +5.5.5.5.5.5.6+-. which in infinte GP 36 91 Probability of B winning

11. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Ball from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, 15 5 5 15 5 5 5 5 5 1 P(A)6 66 6 66 . -.-.-.-.-..which in infinte GP 36 91 Probability of B winning P(B)-:6+6.6.6.6.6 6.6.6.6.6.6.6.6 5 15 5 5 5 1 5 5 5 5 5 5 5 1 30

12. Ques: An urn contains 1 Red, 2 Green, 3 Black balls. 3 People A,B,C in order draw 1 Ball from the urn and put it back after noting the colour. They continue doing it indefinitely unless one who draws a red ball first wins the game. Compute their respective chances of winning the game. Ans Probability of A winning the game, 15 5 5 15 5 5 5 5 5 1 P(A)6 66 6 66 . -.-.-.-.-..which in infinte GP 91 Probability of B winning P(B)-:6+6.6.6.6.6 6.6.6.6.6.6.6.6 5 15 5 5 5 1 5 5 5 5 5 5 5 1 25 Probability of C winning P(C):- 91

13. The probability of getting a sum of 12 in four throws of an ordinary dice, is a)e)3 ber c) ()2 1. (d) None of these 1 (513 d)None ofthese 36 6 n(S) 6x 6 x 6 x 6.

14. The probability of getting a sum of 12 in four throws of an ordinary dice, is 3 :0 ber er b)( )4 ( )2 1 (513 a) d) None of these 36 6 n(S)-6x6x6x6. n (E) = the number of integral solutions of Xi + X2 + X3 + X-12, where 1 sx1 6.., 1 S x4 S 6 = coefficient of x12 in (x + x2 + + x6)"

15. The probability of getting a sum of 12 in four throws of an ordinary dice, is a d) None of these 5 36 6 n(S) 6x 6 x 6 x 6. n (E) the number of integral solutions of x1 X2 X3 x4 12, where 1 XI 6,... 1 X4 S6 - coefficient of x12 in (x + x2 +..+ x")4 = coefficient ofx in = coefficient ofx in (1-x6)4 . ( 3C0 + 4GX + 5C2X2 + .. ) -11Cs-4. 5C2 = 125 6

16. The probability of getting a sum of 12 in four throws of an ordinary dice, is a'er b) ()4 (:)2 5 d) None of these 36 6 n(S) 6x 6 x 6 x 6. n (E) = the number of integral solutions of X1 + X2 + X3 + X4-12, where 1 SX..., 1 Sx4S6 = coefficient of x12 in (x + x2 + + 4 = coefficient ofe in 6 = 11C,-4. 5C2 = 125 P(E) 125 6 x6 x6 x6

17. A die is rolled so that the probability of face i is proportional to i, i - 1, 2,.., 6. The probability an even number occurring when the die is rolled, is a) 7 4 5 b) c) d) None of these 4 7 7 unacademy [.LIVE] Enroll Jagat Chaudhary Follow Qualified IIT-JEE JIT-JAM. Expert faculty for IIT-JEE Mathematics Courses. M.Sc. Ph.D. (MATHEMATICS) IIT Bhubaneswar.Cofounder at Aspiration