If $m$ is chosen at random from the set $\{3,5,8,1... | Free GMAT Practice Question | GMAT Panda

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If m is chosen at random from the set {3, 5, 8, 11} and n is chosen at random from the set {2, 4, 7}, what is the probability that mn 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
$We then note that the product is odd only when both numbers are odd, by Odd \times Odd = Odd.$	$P (product is odd) = P (m is odd and n is odd)$	Theory & Tactics Method Card OE2-A Click to view full details
$We find the probability that m is odd.$	$P (m is odd) = \frac{3}{4}$	Theory & Tactics Method Card PC1-B Click to view full details
$We find the probability that n is odd.$	$P (n is odd) = \frac{1}{3}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then combine these probabilities for the independent choices.$	$P (m is odd and n is odd) = P (m is odd) \times P (n is odd)$
$Multiply the probabilities of m being odd and n being odd.$	$= \frac{3}{4} \times \frac{1}{3}$
$Simplify the multiplication to get the probability that the product is odd.$	$= \frac{1}{4}$	Theory & Tactics Method Card PC1-C Click to view full details
$We then find the probability of an even product.$	$P (product is even) = 1 - \frac{1}{4} = \frac{3}{4}$	Theory & Tactics Method Card PC1-E Click to view full details

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If m is chosen at random from the set {3, 5, 8, 11} and n is chosen at random from the set {2, 4, 7}, what is the probability that mn 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
$We then note that the product is odd only when both numbers are odd, by Odd \times Odd = Odd.$	$P (product is odd) = P (m is odd and n is odd)$	Theory & Tactics Method Card OE2-A Click to view full details
$We find the probability that m is odd.$	$P (m is odd) = \frac{3}{4}$	Theory & Tactics Method Card PC1-B Click to view full details
$We find the probability that n is odd.$	$P (n is odd) = \frac{1}{3}$	Theory & Tactics Method Card PC1-B Click to view full details
$We then combine these probabilities for the independent choices.$	$P (m is odd and n is odd) = P (m is odd) \times P (n is odd)$
$Multiply the probabilities of m being odd and n being odd.$	$= \frac{3}{4} \times \frac{1}{3}$
$Simplify the multiplication to get the probability that the product is odd.$	$= \frac{1}{4}$	Theory & Tactics Method Card PC1-C Click to view full details
$We then find the probability of an even product.$	$P (product is even) = 1 - \frac{1}{4} = \frac{3}{4}$	Theory & Tactics Method Card PC1-E Click to view full details

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E