JEE Advanced 2014 · Paper 2 · Mathematics Q49

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MathematicsSingle correct+3 / -1Question 49 of 60

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

\dfrac12

\dfrac13

\dfrac23

\dfrac34

Answer and worked solution

Official answer: A

Condition. The first girl in the queue needs at least one boy ahead; the second girl (with one girl ahead) needs at least two boys ahead.

Count arrangements of BBBGG ( $\binom52=10$ , equally likely). Valid ones:
$BGBGB,\ BGBBG,\ BBGGB,\ BBGBG,\ BBBGG.$
Any arrangement starting with G fails, and BGGBB fails (the second girl has only one boy ahead).

Probability. $\dfrac5{10}=\dfrac12$ .

(A)

Topics:Classical probability Permutations

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JEE Advanced 2014 · Paper 2, Mathematics question 49