Four fair dice thrown independently 27 times.

Question

Four fair dice thrown independently 27 times. Find the expected number of times at least two dice show a 3 or a 5.

Answer: 11

Accepted Answer

$P(\text{single trial}) = {}^4C_2\left(\dfrac26\right)^2\left(\dfrac46\right)^2+{}^4C_3\left(\dfrac26\right)^3\left(\dfrac46\right)+{}^4C_4\left(\dfrac26\right)^4 = \dfrac{11}{27}$

$$E(X) = 27\times\frac{11}{27}=11$$

Solutions · 1