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

Question

cdquestions Admin · Accepted Answer

The correct is (D); Number of ways of selecting 11 players out of 15 are $^{11}C_{15}$ i.e. $\frac{15\times14\times13\times12}{4\times3\times2\times}=1365$ Number of bowlers = 5 and other players = 10 Favorable outcomes = (3 bowlers and 8 others) or (4 bowlers and 7 others) or (5 bowlers and 6 others) ( $^5C_3$ $\times$ $^{10}C_8$ )+( $^5C_4$ $\times$ $^{10}C_7$ )+( $^5C_5$ $\times$ $^{10}C_6$ ) $(10 × 45) + (5 × 120) + (1 × 210)$ $450 + 600 + 210 = 1260$ $\therefore$ Probability is $\frac{1260}{1365}=\frac{12}{13}$

Answer

$\frac{7}{13}$

Answer

$\frac{6}{13}$

Answer

$\frac{11}{15}$

Answer

$\frac{12}{13}$

List-I	List-II (Adverbs)
(A) P(exactly 2 heads)	(I) \(\frac{1}{4}\)
(B) P(at least 1 head)	(II) \(1\)
(C) P(at most 2 heads)	(III) \(\frac{3}{4}\)
(D) P(exactly 1 head)	(IV) \(\frac{1}{2}\)

LIST-I(EVENT)	LIST-II(PROBABILITY)
(A) The sum of the number is greater than 11	(i) 0
(B) The sum of the number is 4 or less	(ii) 1/15
(C) The sum of the number is 4	(iii) 2/15
(D) The sum of the number is 4	(iv) 3/15

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

The Correct Option is D

Solution and Explanation

Top Questions on Probability

Questions Asked in MAT exam