If x is to be chosen at random from the set 1,2,3,4 and y...

Question

If x is to be chosen at random from the set 1,2,3,4 and y is to be chosen at random from the set 5,6,7, what is the probability that x y will be even?

GMAT Panda · Accepted Answer

The probability is 2/3. (Option D) We first express the probability of an even product in terms of the probability of an odd product. P(product is even) = 1 - P(product is odd) We then note that the product is odd only when both numbers are odd. P(product is odd) = P(x is odd and y is odd) We compute the probability that x is odd. P(x is odd) = 2/4 = 1/2 We compute the probability that y is odd. P(y is odd) = 2/3 We then combine these probabilities for independent choices. P(x is odd and y is odd) = P(x is odd) P(y is odd) = 1/2 2/3 = 1/3 We then find the probability of an even product. P(product is even) = 1 - 1/3 = 2/3

Explanation	Calculations	Help
$We first express the probability of an even product in terms of the probability of an odd product.$	$P (product is even) = 1 - P (product is odd)$
$We then note that the product is odd only when both numbers are odd.$	$P (product is odd) = P (x is odd and y is odd)$
$We compute the probability that x is odd.$	$P (x is odd) = \frac{2}{4} = \frac{1}{2}$
$We compute the probability that y is odd.$	$P (y is odd) = \frac{2}{3}$
$We then combine these probabilities for independent choices.$	$P (x is odd and y is odd) = P (x is odd) \times P (y is odd) = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$
$We then find the probability of an even product.$	$P (product is even) = 1 - \frac{1}{3} = \frac{2}{3}$

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