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(A) When $2$ dice are thrown,the total number of outcomes is $n(S) = 6 	imes 6 = 36$.The possible sums range from $2$ to $12$. The prime numbers in t

Vedclass · Accepted Answer

$\frac{5}{12}$

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(A) When $2$ dice are thrown,the total number of outcomes is $n(S) = 6 	imes 6 = 36$.The possible sums range from $2$ to $12$. The prime numbers in this range are $2, 3, 5, 7, 11$.Let $A$ be the event of getting a sum as a prime number:- Sum $= 2$: $(1, 1)$ $ightarrow 1$ outcome- Sum $= 3$: $(1, 2), (2, 1)$ $ightarrow 2$ outcomes- Sum $= 5$: $(1, 4), (4, 1), (2, 3), (3, 2)$ $ightarrow 4$ outcomes- Sum $= 7$: $(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)$ $ightarrow 6$ outcomes- Sum $= 11$: $(5, 6), (6, 5)$ $ightarrow 2$ outcomesTotal favorable outcomes $n(A) = 1 + 2 + 4 + 6 + 2 = 15$.Therefore,the required probability $P(A) = \frac{n(A)}{n(S)} = \frac{15}{36} = \frac{5}{12}$.

When $2$ dice are thrown,find the probability of getting a sum that is a prime number.

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