Question

Larissa has 5 peanut butter cookies, 7 chocolate chip cookies, 4 sugar cookies, and 9 oatmeal raisin cookies in a jar. If she picks two cookies at random without replacing them, what is the probability that she will choose a peanut butter cookie then a sugar cookie? Express your answer as a fraction.

Short answer

A probability that Larissa will choose a peanut butter cookie then a sugar cookie is$\frac{1}{30}$.

Step-by-step solution

Step 1. Probability.

Find the probability of choosing a peanut butter cookie from a jar.

$\begin{array}{c}{P}_1=\frac{5}{25}\\ =\frac{1}{5}\end{array}$

Step 2. Probability.

As there is no replacement, find the probability of choosing a sugar cookie from 24 cookies in a jar.

$\begin{array}{l}{P}_2=\frac{4}{24}\\ =\frac{1}{6}\end{array}$

Step 3. Find the total probability.

As both the events follow, the probability that she will choose a peanut butter cookie then a sugar cookie is

$\begin{array}{l}P=P_1\cdot P_2\\ =\frac{1}{5}\cdot \frac{1}{6}\\ =\frac{1}{30}\end{array}$

Therefore, that Larissa will choose a peanut butter cookie then a sugar cookie is $\frac{1}{30}$.