Tendulkar is playing a cricket tournament in which each player can play 200 balls and the player who hits maximum sixes wins. Tendulkar hits a six on the first ball, but misses out on the second. After that, the probability that he hits a six is equal the proportion of sixes that he has hit so far. For example, at the third ball, the probability is 12. (a) What is the probability that Tendulkar hits only one six? (b) What is the probability that Tendulkar hits 100 sixes?

Question

Tendulkar is playing a cricket tournament in which each player can play 200 balls and the player who hits maximum sixes wins. Tendulkar hits a six on the first ball, but misses out on the second.  After that, the probability that he hits a six is equal the proportion of sixes that he has hit so far. For example, at the third ball, the probability is 12.  (a) What is the probability that Tendulkar hits only one six?  (b) What is the probability that Tendulkar hits 100 sixes?

Sevensis1977 · Accepted Answer

Given data, The number of balls each player has to play is 200. The player who hits maximum number of six will win. Step 1 a) The probability that Tendulkar hits the one six is, The probability that he hits six at 3rd ball is, P=12 The probability that he hits six at 4th ball is, P=23 Similarly, the probability that he hits six at 200th ball is, P=198199. The probability of one six in 200 ball is, P=198199×197198×……×23×12 =1199 Step 2 b)The probability that Tendulkar hits 100 hits is, Consider, P(k, n) be the probability of Tendulkar hitting k sixes in n balls. Here, 0&amp;lt;k&amp;lt;n The probability is calculated as, P(k,n)=kn−1 Here, k=100 n=200 Substituting the values then, P(100,200)=100199

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