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

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 $X$ be the sum of the numbers on the two dice. The possible values for $X$ range from $2$ to $12$. The prime numbers in this range are $2, 3, 5, 7, 11$. We calculate the number of outcomes for each sum: - $X=2$: $(1,1) ightarrow 1$ outcome - $X=3$: $(1,2), (2,1) ightarrow 2$ outcomes - $X=5$: $(1,4), (2,3), (3,2), (4,1) ightarrow 4$ outcomes - $X=7$: $(1,6), (2,5), (3,4), (4,3), (5,2), (6,1) ightarrow 6$ outcomes - $X=11$: $(5,6), (6,5) ightarrow 2$ 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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