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

Answer: (B)

$\frac{1}{3}$

Answer 2

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:

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