Two balanced dice are rolled simultaneously. | vedclass

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Question

(A) The total number of outcomes when two dice are rolled is $6 	imes 6 = 36$.The possible sums of the numbers on the two dice range from $2$ to $12$

Vedclass · Accepted Answer

$\frac{5}{12}$

Vedclass · Answer

(A) The total number of outcomes when two dice are rolled is $6 	imes 6 = 36$.The possible sums of the numbers on the two dice range from $2$ to $12$. The prime numbers in this range are $2, 3, 5, 7,$ and $11$.Let us list the favorable outcomes for each prime sum:- Sum $= 2$: $(1, 1)$ [$1$ outcome]- Sum $= 3$: $(1, 2), (2, 1)$ [$2$ outcomes]- Sum $= 5$: $(1, 4), (2, 3), (3, 2), (4, 1)$ [$4$ outcomes]- Sum $= 7$: $(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)$ [$6$ outcomes]- Sum $= 11$: $(5, 6), (6, 5)$ [$2$ outcomes]Total number of favorable outcomes $= 1 + 2 + 4 + 6 + 2 = 15$.Therefore,the required probability $= \frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{15}{36} = \frac{5}{12}$.

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