If $p$ is chosen at random from the set $\{2,3,5,7... | Free GMAT Practice Question | GMAT Panda

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If p is chosen at random from the set {2, 3, 5, 7} and q is chosen at random from the set {4, 6, 9}, what is the probability that p \times q will be even?

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

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D

If p is chosen at random from the set {2, 3, 5, 7} and q is chosen at random from the set {4, 6, 9}, what is the probability that p \times q will be even?

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

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D