The mean of the numbers obtained on throwing | vedclass

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(B) Let $X$ be the random variable representing the number obtained on the die.The total number of faces on the die is $6$.The probabilities of obtain

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$2$

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(B) Let $X$ be the random variable representing the number obtained on the die.The total number of faces on the die is $6$.The probabilities of obtaining each number are:$P(X=1) = \frac{3}{6} = \frac{1}{2}$$P(X=2) = \frac{2}{6} = \frac{1}{3}$$P(X=5) = \frac{1}{6}$The mean (expected value) $E(X)$ is calculated as $\sum x_i P(x_i)$:$E(X) = (1 	imes \frac{1}{2}) + (2 	imes \frac{1}{3}) + (5 	imes \frac{1}{6})$$E(X) = \frac{1}{2} + \frac{2}{3} + \frac{5}{6}$To add these fractions,find the common denominator,which is $6$:$E(X) = \frac{3}{6} + \frac{4}{6} + \frac{5}{6}$$E(X) = \frac{3+4+5}{6} = \frac{12}{6} = 2$Thus,the mean is $2$. The correct answer is $B$.

The mean of the numbers obtained on throwing a die having $1$ on three faces,$2$ on two faces,and $5$ on one face is

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