If two regular six-sided dice are thrown,the | vedclass

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(C) When two six-sided dice are thrown,the total number of possible outcomes is $6^2 = 36$.The possible sums range from $2$ to $12$.The prime numbers

Vedclass · Accepted Answer

$\frac{5}{12}$

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(C) When two six-sided dice are thrown,the total number of possible outcomes is $6^2 = 36$.The possible sums range from $2$ to $12$.The prime numbers between $2$ and $12$ are $\{2, 3, 5, 7, 11\}$.We list the favorable outcomes for each prime sum:- Sum $= 2$: $(1, 1)$ [$1$ outcome]- Sum $= 3$: $(1, 2), (2, 1)$ [$2$ outcomes]- Sum $= 5$: $(1, 4), (4, 1), (2, 3), (3, 2)$ [$4$ outcomes]- Sum $= 7$: $(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)$ [$6$ outcomes]- Sum $= 11$: $(5, 6), (6, 5)$ [$2$ outcomes]Total number of favorable outcomes $= 1 + 2 + 4 + 6 + 2 = 15$.The probability is given by $\frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{15}{36} = \frac{5}{12}$.

If two regular six-sided dice are thrown,the probability that the sum will be a prime number is

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