View source for GATE2009 q21 ← GATE2009 q21

An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than $3$ is $0.75$, which one of the following options is closest to the probability that the face value exceeds $3$?

(A) 0.453

(B) 0.468

(C) 0.485

(D) 0.492

Solution by Happy Mittal[edit]

Let $P(even) = x$, so $P(odd) = 90\%$ of $x$

$= 9x/10$,

But $P(even) + P(odd) = 1$,

so $x + 9x/10 = 1$, $x = 10/19$

$=P(even)$

Since probability of any even number is same,

$P(2) = P(4) = P(6) = 10/(19*3) = 10/57$

Now $P$(even and exceeds $3$) = $P$(exceeds $3$) * $P$(even|exceeds $3$). So

$P$(exceeds $3$) = $P$(even and exceeds $3$)/$P$(even|exceeds $3$)

$= (P(4) + P(6))/0.75 $

$= (20/57)/0.75 = 0.468$

So option (B) is correct.