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(B) When two dice are thrown,the total number of possible outcomes is $n(S) = 6 	imes 6 = 36$.The product of two numbers is odd only if both numbers

Vedclass · Accepted Answer

$\frac{3}{4}$

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(B) When two dice are thrown,the total number of possible outcomes is $n(S) = 6 	imes 6 = 36$.The product of two numbers is odd only if both numbers are odd. The odd numbers on a die are $\{1, 3, 5\}$.The number of outcomes where both dice show an odd number is $3 	imes 3 = 9$.These outcomes are: $(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)$.The product is even if it is not odd. Therefore,the number of outcomes with an even product is $n(E) = n(S) - n(	ext{odd product}) = 36 - 9 = 27$.The probability of getting an even product is $P(E) = \frac{n(E)}{n(S)} = \frac{27}{36} = \frac{3}{4}$.

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

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