Question

Two dice are thrown simultaneously. If $X$ denotes the number of fours, then the expectation of $X$ will be:

• A. $\frac{5}{9}$
• B. $\frac{1}{3}$
• C. $\frac{4}{7}$
• D. $\frac{3}{8}$

Answer 1

The Correct Option is B

Each die has a probability of \( \frac{1}{6} \) of showing a four. The expectation of \( X \) (the number of fours) is the sum of the expectations for each die:

\[ E(X) = E(X_1) + E(X_2), \]

where:

\[ E(X_1) = \frac{1}{6}, \quad E(X_2) = \frac{1}{6}. \]

Thus:

\[ E(X) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}. \]