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(B) Let $A$ be the event that the number $4$ appears at least once,and $B$ be the event that the sum of the numbers is $6$.The sample space for the su

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(B) Let $A$ be the event that the number $4$ appears at least once,and $B$ be the event that the sum of the numbers is $6$.The sample space for the sum being $6$ is $B = \{(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)\}$.Thus,the total number of outcomes in $B$ is $n(B) = 5$.The event $A \cap B$ represents the outcomes where the sum is $6$ $AND$ the number $4$ appears at least once.Looking at the set $B$,the outcomes containing $4$ are $(2, 4)$ and $(4, 2)$.So,$A \cap B = \{(2, 4), (4, 2)\}$,which means $n(A \cap B) = 2$.The conditional probability is given by $P(A|B) = \frac{n(A \cap B)}{n(B)} = \frac{2}{5}$.

$A$ die is thrown twice. If the sum of the numbers obtained is $6$,what is the probability that the number $4$ appears at least once?

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