First slide
Introduction to probability
Question

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

Moderate
Solution

The total number of ways of choosing 11 players out of 15 is  15C11. A team of 11 players containing at least 3 bowlers can be chosen in the following mutually exclusive ways:

(I) Three bowlers out of 5 bowlers and 8 other players out of the remaining 10 players.

(II) Four bowlers out of 5 bowlers and 7 other players out of the remaining 10 players.

(III) Five bowlers out of 5 bowlers and 6 other players out of the remaining 10 players.

So, required probability is

P(I) + P(II) + P(III)

= 5C3×10C8 15C11+ 5C4×10C7 15C11+ 5C5×10C6 15C11=12601365=1213

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