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(C) Let $S$ be the sample space of throwing two dice,where $n(S) = 36$. Let $A$ be the event that $5$ appears on at least one die. The outcomes for $A

Vedclass · Accepted Answer

$\frac{3}{11}$

Vedclass · Answer

(C) Let $S$ be the sample space of throwing two dice,where $n(S) = 36$. Let $A$ be the event that $5$ appears on at least one die. The outcomes for $A$ are: $(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5)$. Thus,$n(A) = 11$. Let $B$ be the event that the sum is $10$ or greater. The outcomes for $A \cap B$ (sum $\ge 10$ and at least one $5$) are: $(5, 5), (5, 6), (6, 5)$. Thus,$n(A \cap B) = 3$. The conditional probability $P(B|A) = \frac{n(A \cap B)}{n(A)} = \frac{3}{11}$.

$A$ pair of dice is thrown. If $5$ appears on at least one of the dice,then the probability that the sum is $10$ or greater is:

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