A six-faced unbiased die is thrown twice and | vedclass

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(B) Let $S$ be the sample space of outcomes where the sum of the two dice is $7$. The possible outcomes are: $S = \{(1, 6), (6, 1), (2, 5), (5, 2), (3

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$1/3$

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(B) Let $S$ be the sample space of outcomes where the sum of the two dice is $7$. The possible outcomes are: $S = \{(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)\}$ Thus,the total number of outcomes $n(S) = 6$. Let $E$ be the event that the number $3$ appears at least once. The outcomes in $E$ are: $E = \{(3, 4), (4, 3)\}$ Thus,the number of favorable outcomes $n(E) = 2$. The required probability is $P(E) = \frac{n(E)}{n(S)} = \frac{2}{6} = \frac{1}{3}$.

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

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