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(A) When two dice are rolled,the total number of possible outcomes is $6 	imes 6 = 36$. Let $S$ be the sum of the numbers on the two dice. The possib

Vedclass · Accepted Answer

$\frac{5}{12}$

Vedclass · Answer

(A) When two dice are rolled,the total number of possible outcomes is $6 	imes 6 = 36$. Let $S$ be the sum of the numbers on the two dice. The possible values for $S$ range from $2$ to $12$. The prime numbers between $2$ and $12$ are $2, 3, 5, 7, 11$. We list the outcomes for each prime sum: - Sum $= 2$: $(1, 1)$ $ightarrow 1$ outcome - Sum $= 3$: $(1, 2), (2, 1)$ $ightarrow 2$ outcomes - Sum $= 5$: $(1, 4), (2, 3), (3, 2), (4, 1)$ $ightarrow 4$ outcomes - Sum $= 7$: $(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)$ $ightarrow 6$ outcomes - Sum $= 11$: $(5, 6), (6, 5)$ $ightarrow 2$ outcomes Total favorable outcomes $= 1 + 2 + 4 + 6 + 2 = 15$. Probability $= \frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{15}{36} = \frac{5}{12}$.

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

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