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(D) The set for $x$ is $\{1, 2, 3, 4\}$ and the set for $y$ is $\{5, 6, 7\}$.Total number of possible outcomes is $4 	imes 3 = 12$.The product $xy$ i

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$\frac{2}{3}$

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(D) The set for $x$ is $\{1, 2, 3, 4\}$ and the set for $y$ is $\{5, 6, 7\}$.Total number of possible outcomes is $4 	imes 3 = 12$.The product $xy$ is even if at least one of $x$ or $y$ is even.Alternatively,$xy$ is odd only if both $x$ and $y$ are odd.Odd values in $x$ are $\{1, 3\}$ (count = $2$).Odd values in $y$ are $\{5, 7\}$ (count = $2$).Number of outcomes where $xy$ is odd = $2 	imes 2 = 4$.Number of outcomes where $xy$ is even = $	ext{Total outcomes} - 	ext{Odd outcomes} = 12 - 4 = 8$.Probability that $xy$ is even = $\frac{8}{12} = \frac{2}{3}$.

If $x$ is chosen at random from the set $\{1, 2, 3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$,then the probability that $xy$ will be even is

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