Chapter 12, Problem 14STP

To determine

To find: the probability that she will choose a peanut butter cookie than a sugar cookie.

Answer to Problem 14STP

The probability that she will choose a peanut butter cookie than a sugar cookie is $\frac{3}{200}$ .

Explanation of Solution

Given information:

Larissa ha peanut butter, chocolate chip cookies, sugar cookies and catmeal raisin cookies respectively $5,7,4,9$ .

Calculation: To find the probability that she will choose butter cookies and than sugar cookies, first choose $1$ butter cookie from the total butter cookies and choose $1$ sugar cookie from the total sugar cookie and divide it by choosing $2$ cookies from total cookies,

  $\begin{array}{l}\frac{C_1^5+C_1^4}{C_2^{25}}\\ \frac{\frac{5!}{\left(5-1\right)!}+\frac{4!}{\left(4-1\right)!}}{\frac{25!}{\left(25-2\right)!}}\text{ [}{C}_r^n=\frac{n!}{\left(n-r\right)!}]\\ \frac{\frac{5!}{4!}+\frac{4!}{3!}}{\frac{25!}{23!}}\text{ [subtract]}\\ \frac{\frac{5·4!}{4!}+\frac{4·3!}{3!}}{\frac{25·24·23!}{23!}}\text{ [expand factorial]}\\ \frac{5+4}{25·24}\text{ [divide out common factors]}\\ \frac{9}{600}\text{ [add and multiply]}\\ \frac{3}{200}\text{ [simplify]}\end{array}$

Thus, the probability is $\frac{3}{200}$ .