Chapter 11.5, Problem 31SR

To determine

To find: The probability that is snows 3 out of the next 7 days.

Answer to Problem 31SR

The probability that it will snow 3 out of 7 days is 0.173 or 17.3%.

Explanation of Solution

Given:

The chances that it will snow is 25%.

Calculation:

Consider the probability that it will not snow is,

  $\begin{array}{c}q=1-0.25\\ =0.75\end{array}$

Consider the number of days in the week is.

  $n=7$

Then, by the binomial probability formula,

  $P\left(X\right){=}_n{C}_X{p}^X{q}^{n-x}$

Then,

  $\begin{array}{c}P\left(X\right){=}_7{C}_3{\left(0.25\right)}^3{\left(0.75\right)}^{7-3}\\ =\frac{7!}{3!\left(7-3\right)!}{\left(0.25\right)}^3{\left(0.75\right)}^{7-3}\\ =\frac{5040}{6\left(24\right)}\left(0.015625\right)\left(0.31640625\right)\\ =0.173\end{array}$

Thus, the probability that it will snow 3 out of 7 days is 0.173 or 17.3%.