Two dice are thrown. What is the probability | vedclass

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(B) Let $A$ be the event that the sum of the numbers is $11$,and $B$ be the event that $5$ appears on the first die.The sample space for the first die

Vedclass · Accepted Answer

$\frac{1}{6}$

Vedclass · Answer

(B) Let $A$ be the event that the sum of the numbers is $11$,and $B$ be the event that $5$ appears on the first die.The sample space for the first die showing $5$ is $S = \{(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)\}$.The total number of outcomes in $B$ is $n(B) = 6$.The event $A \cap B$ is the outcome where the sum is $11$ and the first die is $5$,which is $\{(5, 6)\}$.The number of favorable outcomes is $n(A \cap B) = 1$.The conditional probability is $P(A|B) = \frac{n(A \cap B)}{n(B)} = \frac{1}{6}$.

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$,given that $5$ appears on the first die?

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