1. **Problem statement:** Tate has a bag with 7 oatmeal cookies, 5 sugar cookies, and 4 peanut butter cookies, total 16 cookies. He selects one cookie, eats it, then selects another cookie. 2. **Is this an example of independence?** No, because eating the first cookie changes the total number of cookies and the composition of the bag, affecting the probability of the second selection. So, the events are dependent. 3. **Find the probability that Tate selects a peanut butter cookie first AND an oatmeal cookie second.** - Probability of selecting a peanut butter cookie first: $\frac{4}{16}$ - After eating one peanut butter cookie, remaining cookies: 15 total, with 7 oatmeal cookies still there. - Probability of selecting an oatmeal cookie second: $\frac{7}{15}$ 4. **Calculate combined probability:** $$ P(\text{peanut butter first AND oatmeal second}) = \frac{4}{16} \times \frac{7}{15} = \frac{4 \times 7}{16 \times 15} = \frac{28}{240} = \frac{7}{60} $$ 5. **Summary:** - The events are dependent. - The probability of selecting a peanut butter cookie first and an oatmeal cookie second is $\frac{7}{60}$.