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(B) Let $A$ be the event that the sum of the numbers is greater than $7$.Let $B$ be the event that $4$ appears on the first die.The sample space for t

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$\frac{1}{2}$

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(B) Let $A$ be the event that the sum of the numbers is greater than $7$.Let $B$ be the event that $4$ appears on the first die.The sample space for the first die showing $4$ is $S = \{(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)\}$.The total number of outcomes in $B$ is $n(B) = 6$.The outcomes where the sum is greater than $7$ are $(4, 4), (4, 5), (4, 6)$.Thus,the number of favorable outcomes is $n(A \cap B) = 3$.The conditional probability is $P(A|B) = \frac{n(A \cap B)}{n(B)} = \frac{3}{6} = \frac{1}{2}$.

In a single throw of two dice,what is the probability of obtaining a sum of numbers greater than $7$,given that $4$ appears on the first die?

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