When two dice are rolled,what is the probabil | vedclass

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(D) When two dice are rolled,the total number of outcomes is $n(S) = 6 	imes 6 = 36$.The sum of the numbers on the two dice can range from $2$ to $12

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(D) When two dice are rolled,the total number of outcomes is $n(S) = 6 	imes 6 = 36$.The sum of the numbers on the two dice can range from $2$ to $12$.The sums that are multiples of $3$ are $3, 6, 9,$ and $12$.Let $E$ be the event that the sum is a multiple of $3$. The favorable outcomes are:- Sum $= 3$: $(1, 2), (2, 1)$- Sum $= 6$: $(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)$- Sum $= 9$: $(3, 6), (4, 5), (5, 4), (6, 3)$- Sum $= 12$: $(6, 6)$Counting these outcomes,we get $n(E) = 2 + 5 + 4 + 1 = 12$.The required probability is $P(E) = \frac{n(E)}{n(S)} = \frac{12}{36} = \frac{1}{3}$.

When two dice are rolled,what is the probability that the sum of the numbers appearing is a multiple of $3$?

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