A pair of dice is thrown 5 times.

Question

A pair of dice is thrown 5 times. A total of 5 is a "success". If the probability of at least 4 successes is $\dfrac{k}{3^{11}}$, find $k$.

Accepted Answer

$P(\text{success})=\dfrac{4}{36}=\dfrac19$.

$$P(\ge4) = {}^5C_4\left(\frac19\right)^4\frac89+{}^5C_5\left(\frac19\right)^5 = \frac{41}{9^5}=\frac{41}{3^{10}}=\frac{123}{3^{11}} \implies k=123$$

Solutions · 1