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(B) Let $A$ be the event that $4$ appears on the first die.The sample space for the first die showing $4$ is: $(4, 1), (4, 2), (4, 3), (4, 4), (4, 5),

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$\frac{1}{2}$

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(B) Let $A$ be the event that $4$ appears on the first die.The sample space for the first die showing $4$ is: $(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)$.There are $6$ possible outcomes in this reduced sample space.Let $B$ be the event that the sum of the numbers is greater than $7$.We look for outcomes $(4, x)$ such that $4 + x > 7$,which implies $x > 3$.The favorable outcomes are $(4, 4), (4, 5), (4, 6)$.There are $3$ favorable outcomes.The required probability is $\frac{	ext{Number of favorable outcomes}}{	ext{Total outcomes in reduced sample space}} = \frac{3}{6} = \frac{1}{2}$.

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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