Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) - $\frac{1}{3}$
| $X$ | 0 | 1 | 2 |
| $P(X)$ | ${^2C}_0(\frac{5}{6})^2=\frac{25}{36}$ | ${^2C}_1(\frac{1}{6})(\frac{5}{6})=\frac{10}{36}$ | ${^2C}_2(\frac{1}{6})^2=\frac{1}{36}$ |
$E(X)=0×\frac{25}{36}+1×\frac{10}{36}+2×\frac{1}{36}$
$=\frac{10+2}{36}=\frac{1}{3}$