CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. M.P.Keshari Probability 13.1. Conditional Probability. Q.1. A and B toss a coin alternately till one of them gets a head and wins the game. If A starts first, find the probability that B will win the game. Solution : We have, P(H) = 1/2 and P(T) = 1/2 . [Ans.] Q.2. A and B throw two dice simultaneously turn by turn. A will win if he throws a total of 5, B will win if he throws a doublet. Find the probability that B will win the game, though A started it. Solution : Let the event of winning A be denoted by ‘A’ and that of B by ‘B’.P(A) = 4/36 = 1/9 and P(not A) = 1 – 1/9 = 8/9.[(1, 4), (2, 3), (3, 2), (4, 1)] P(B) = 6/36 = 1/6 and P(notB) = 5/6. [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)] Now A starts the game. Therefore, P(B) = P(not A)P(B) + P(not A)P(not B)P(not A)P(B) + P(not A)P(not B)P(not A)P(not B)P(not A)P(B) + -------- = 8/9×1/6 + 8/9×5/6×8/9×1/6 + 8/9×5/6×8/9×5/6×8/9×1/6 + --------- [This in an infinite G.P.] a = 8/9×1/6 and r = 5/6×8/9 < 1. Therefore, P(B) = a/(1 – r) = [8/9×1/6]/[1 – (5/6×8/9)] = 8/(54 – 40) = 8/14 = 4/7.[Ans.] Q.3. Two dice are rolled once. Find the probability that :
Solution : Total number of cases are 6×6 = 36.
Paper By Mr. M.P.Keshari |
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