If $x$ is to be chosen at random from the set $\{1... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

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?

Explanation	Calculations	Help
$We first express the probability of an even product in terms of the probability of an odd product.$	$P (product is even) = 1 - P (product is odd)$	Theory & Tactics Method Card PC1-E Click to view full details
$We then note that the product is odd only when both numbers are odd.$	$P (product is odd) = P (x is odd and y is odd)$
$We compute the probability that x is odd.$	$P (x is odd) = \frac{2}{4} = \frac{1}{2}$	Theory & Tactics Method Card PC1-B Click to view full details
$We compute the probability that y is odd.$	$P (y is odd) = \frac{2}{3}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then combine these probabilities for independent choices.$	$P (x is odd and y is odd) = P (x is odd) \times P (y is odd) = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$	Theory & Tactics Method Card PC1-C Click to view full details
$We then find the probability of an even product.$	$P (product is even) = 1 - \frac{1}{3} = \frac{2}{3}$	Theory & Tactics Method Card PC1-E Click to view full details

Scroll horizontally to view all columns

The probability is \frac{2}{3} . (Option D)

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?

Explanation	Calculations	Help
$We first express the probability of an even product in terms of the probability of an odd product.$	$P (product is even) = 1 - P (product is odd)$	Theory & Tactics Method Card PC1-E Click to view full details
$We then note that the product is odd only when both numbers are odd.$	$P (product is odd) = P (x is odd and y is odd)$
$We compute the probability that x is odd.$	$P (x is odd) = \frac{2}{4} = \frac{1}{2}$	Theory & Tactics Method Card PC1-B Click to view full details
$We compute the probability that y is odd.$	$P (y is odd) = \frac{2}{3}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then combine these probabilities for independent choices.$	$P (x is odd and y is odd) = P (x is odd) \times P (y is odd) = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$	Theory & Tactics Method Card PC1-C Click to view full details
$We then find the probability of an even product.$	$P (product is even) = 1 - \frac{1}{3} = \frac{2}{3}$	Theory & Tactics Method Card PC1-E Click to view full details

Scroll horizontally to view all columns

The probability is \frac{2}{3} . (Option D)