The bag contains: 4 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies.
Therefore, there is a total of 24 cookies.
Thus, the probability of selecting an oatmeal cookie (8) from the bag (24) is: 1/3
[tex]P_1=\frac{8}{24}=\frac{1}{3}\approx0.3333\ldots[/tex]After she eats this cookie, there are 23 cookies left.
Now, the probability of selecting a peanut butter cookie (4) from the bag (23) is: 4/23
[tex]P_2=\frac{4}{23}=0.17391\approx0.1739[/tex]Now, the probability of these two events to happen, is the following: 4/69
[tex]\begin{gathered} P_{1\&2}=P_1\cdot P_2=\frac{8}{24}\cdot\frac{4}{23} \\ =\frac{1}{3}\cdot\frac{4}{23} \\ =\frac{4}{69} \\ \approx0.0580 \end{gathered}[/tex]