Chapter 7, Problem AP2.5CPT

To determine

To find: the probability that a 6 occurs on exactly one of the rolls.

Answer to Problem AP2.5CPT

  $4\times \frac{1}{6}\times {\left(\frac{5}{6}\right)}^3$

Explanation of Solution

Formula used:

  $P\left(X=r\right)=C{}_1{\left(p\right)}^r{\left(q\right)}^{n-r}$

Calculation:

Since each die roll is independent

  $X~binomial\left(4,1/6\right)$

  $\begin{array}{c}P\left(X=1\right)=C{}_1{\left(\frac{1}{6}\right)}^1{\left(\frac{5}{6}\right)}^3\\ =4\times \frac{1}{6}\times {\left(\frac{5}{6}\right)}^3\end{array}$

Hence, the correct option is (c)