Two integers are chosen at random and multipl | vedclass

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Question

(B) Let the two integers be $x$ and $y$. Each integer can be either even $(E)$ or odd $(O)$.There are $4$ possible outcomes for the parity of the two

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(B) Let the two integers be $x$ and $y$. Each integer can be either even $(E)$ or odd $(O)$.There are $4$ possible outcomes for the parity of the two integers: $(E, E), (E, O), (O, E), (O, O)$.Each outcome is equally likely with a probability of $\frac{1}{4}$.$1$. If both integers are even $(E, E)$,the product is even.$2$. If one is even and one is odd $(E, O)$ or $(O, E)$,the product is even.$3$. If both integers are odd $(O, O)$,the product is odd.The product is even in $3$ out of the $4$ cases: $(E, E), (E, O), (O, E)$.Therefore,the required probability is $\frac{3}{4}$.

Two integers are chosen at random and multiplied. The probability that the product is an even integer is

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