If $m$ is chosen at random from the set $\{1,2,3,5... | 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 m is chosen at random from the set {1, 2, 3, 5} and n is chosen at random from the set {4, 6, 7, 9}, what is the probability that mn will be even?

Explanation	Calculations	Help
$We first express the probability of an even product as one minus the probability of an odd product.$	$P (product is even) = 1 - P (product is odd)$	Theory & Tactics Method Card PC1-E Click to view full details
$We note that the product is odd only when both factors are odd.$	$P (product is odd) = P (m is odd and n is odd)$
$We then find the probability that m is odd.$	$P (m is odd) = \frac{3}{4}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then find the probability that n is odd.$	$P (n is odd) = \frac{2}{4} = \frac{1}{2}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then multiply these probabilities because the choices of m and n are independent.$	$P (m is odd and n is odd) = P (m is odd) \times P (n is odd) = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$	Theory & Tactics Method Card PC1-C Click to view full details
$We then find the probability of an even product by subtracting the odd case from 1.$	$P (product is even) = 1 - \frac{3}{8} = \frac{5}{8}$	Theory & Tactics Method Card PC1-E Click to view full details

Scroll horizontally to view all columns

D

If m is chosen at random from the set {1, 2, 3, 5} and n is chosen at random from the set {4, 6, 7, 9}, what is the probability that mn will be even?

Explanation	Calculations	Help
$We first express the probability of an even product as one minus the probability of an odd product.$	$P (product is even) = 1 - P (product is odd)$	Theory & Tactics Method Card PC1-E Click to view full details
$We note that the product is odd only when both factors are odd.$	$P (product is odd) = P (m is odd and n is odd)$
$We then find the probability that m is odd.$	$P (m is odd) = \frac{3}{4}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then find the probability that n is odd.$	$P (n is odd) = \frac{2}{4} = \frac{1}{2}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then multiply these probabilities because the choices of m and n are independent.$	$P (m is odd and n is odd) = P (m is odd) \times P (n is odd) = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$	Theory & Tactics Method Card PC1-C Click to view full details
$We then find the probability of an even product by subtracting the odd case from 1.$	$P (product is even) = 1 - \frac{3}{8} = \frac{5}{8}$	Theory & Tactics Method Card PC1-E Click to view full details

Scroll horizontally to view all columns

D