Probability Question 339
Question: A cricket club has 15 members, of whom only 5 can bowl. If the name of 15 members are put into a box and 11 are drawn at random, then the probability of getting an eleven contain at least 3 bowlers is
Options:
A) 7/13
B) 6/13
C) 11/15
D) 12/13
Show Answer
Answer:
Correct Answer: D
Solution:
The total number of ways of choosing 11 players out of 15 is $ ^{15}C_{11}. $
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 $ =P(I)+P(II)+P(III) $
$ =\frac{^{5}C_3{{\times }^{10}}C_8}{^{15}C_{11}}+\frac{^{5}C_4{{\times }^{10}}C_7}{^{15}C_{11}}+\frac{^{5}C_5{{\times }^{10}}C_6}{^{15}C_{11}}=\frac{12}{13}. $
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