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(B) Let the first observation be from the black die and the second from the red die.When two dice (one black and one red) are rolled,the sample space

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$1/3$

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(B) Let the first observation be from the black die and the second from the red die.When two dice (one black and one red) are rolled,the sample space $S$ has $6 	imes 6 = 36$ outcomes.Let $A$ be the event of obtaining a sum greater than $9$.$A = \{(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)\}$Let $B$ be the event that the black die results in a $5$.$B = \{(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)\}$The intersection of these events is $A \cap B = \{(5,5), (5,6)\}$.The number of elements in $B$ is $n(B) = 6$,and the number of elements in $A \cap B$ is $n(A \cap B) = 2$.The conditional probability $P(A|B)$ is given by:$P(A|B) = \frac{n(A \cap B)}{n(B)} = \frac{2}{6} = \frac{1}{3}$.

$A$ black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than $9,$ given that the black die resulted in a $5$.

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