Three numbers are chosen at random without replacement from $\{1,2,3, \ldots \ldots 8\}$. The probability that their minimum is 3, given that their maximum is 6, is

JEE Main · 2012 · 29 Apr 2012 · Offline · Probability

Three numbers are chosen at random without replacement from

{1, 2, 3, \dots\dots 8}

. The probability that their minimum is 3, given that their maximum is 6, is

Answer: (B)

Condition on the maximum being

6

: the three numbers include

6

together with two more drawn from

{1, 2, 3, 4, 5}

, which can happen in

(2 5) = 10

ways. Of these, the ones whose minimum is also

3

must contain both

3

and

6

, with the third number taken from

{4, 5}

, giving

(1 2) = 2

ways. The required conditional probability is

\frac{2}{10} = \frac{1}{5}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option