Multiple choice

A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn random, then the chance of obtaining an eleven containing at least 3 bowlers is

  1. $\displaystyle \frac{7}{13}$
  2. $\displaystyle \frac{11}{15}$
  3. $\displaystyle \frac{12}{13}$

  4. None of these.
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C Correct answer
AI explanation

The total number of ways to choose 11 players from 15 is 15C11 = 1365. The probability of getting at least 3 bowlers is found by subtracting the probabilities of getting exactly 0, 1, or 2 bowlers from 1. The number of ways to choose 0 bowlers and 11 batsmen is 5C0 times 10C11 = 0, the ways for 1 bowler and 10 batsmen is 5C1 times 10C10 = 5, and the ways for 2 bowlers and 9 batsmen is 5C2 times 10C9 = 10 times 10 = 100. The probability of getting fewer than 3 bowlers is (5 + 100)/1365 = 105/1365 = 1/13. Subtracting this from 1 gives 1 - 1/13 = 12/13.

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