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(C) Let $E_1$ be the event that either of the dice shows $2$. Let $E_2$ be the event that the sum of the numbers on the dice is $6$. The sample space

Vedclass · Accepted Answer

$\frac{2}{5}$

Vedclass · Answer

(C) Let $E_1$ be the event that either of the dice shows $2$. Let $E_2$ be the event that the sum of the numbers on the dice is $6$. The sample space for the sum being $6$ is $E_2 = \{(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)\}$. Thus,the number of outcomes in $E_2$ is $n(E_2) = 5$. The outcomes where either of the dice shows $2$ given the sum is $6$ are $E_1 \cap E_2 = \{(2, 4), (4, 2)\}$. Thus,the number of outcomes in $E_1 \cap E_2$ is $n(E_1 \cap E_2) = 2$. The conditional probability is given by $P(E_1 | E_2) = \frac{n(E_1 \cap E_2)}{n(E_2)} = \frac{2}{5}$.

$A$ pair of dice is thrown. Then the probability that either of the dice shows $2$ when their sum is $6$ is

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