Soraya buys a bag of cookies that contains 5 chocolate chip cookies, 9 peanut butter cookies, 6 sugar cookies, and 6 oatmeal cookies.

What is the probability that Soraya reaches in the bag and randomly selects an oatmeal cookie from the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie? Round your answer to four decimal places.

To calculate the probability that Soraya first selects an oatmeal cookie and then a sugar cookie, we'll follow these steps:

1. **Total number of cookies in the bag initially:**
   \[
   5 \text{ (chocolate chip)} + 9 \text{ (peanut butter)} + 6 \text{ (sugar)} + 6 \text{ (oatmeal)} = 26 \text{ cookies}
   \]

2. **Step 1: Probability of selecting an oatmeal cookie:**
   The probability of picking an oatmeal cookie on the first selection is:
   \[
   P(\text{oatmeal}) = \frac{6}{26}
   \]

3. **Step 2: Probability of selecting a sugar cookie after eating the oatmeal cookie:**
   After Soraya eats the oatmeal cookie, 25 cookies remain in the bag, with 6 sugar cookies still present. The probability of picking a sugar cookie now is:
   \[
   P(\text{sugar}) = \frac{6}{25}
   \]

4. **Step 3: Total probability:**
   To find the combined probability of both events (picking an oatmeal cookie and then a sugar cookie), we multiply the probabilities of each event:
   \[
   P(\text{oatmeal and sugar}) = P(\text{oatmeal}) \times P(\text{sugar}) = \frac{6}{26} \times \frac{6}{25}
   \]

Now let's calculate that:

\[
P(\text{oatmeal and sugar}) = \frac{6 \times 6}{26 \times 25} = \frac{36}{650} \approx 0.0554
\]

Thus, the probability that Soraya selects an oatmeal cookie, eats it, and then selects a sugar cookie is approximately **0.0554**.

Would you like further details or clarifications?

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Here are 5 related questions to expand on the concept:
1. What is the probability of picking a chocolate chip cookie, then a peanut butter cookie?
2. What is the probability of selecting two sugar cookies in a row?
3. How does the probability change if the bag had 30 cookies instead of 26?
4. What is the probability of selecting a non-oatmeal cookie first and then a sugar cookie?
5. How do probabilities change if Soraya puts back the cookie before selecting again?

**Tip:** When calculating probabilities involving multiple events, always check if the events are independent (with replacement) or dependent (without replacement).

Soraya buys a bag of cookies that contains 5 chocolate chip cookies, 9 peanut butter cookies, 6 sugar cookies, and 6 oatmeal cookies. What is the probability that Soraya reaches in the bag and randomly selects an oatmeal cookie from the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie? Round your answer to four decimal places.

Discover how to calculate the probability of selecting an oatmeal cookie followed by a sugar cookie from a bag of 26 cookies. This solution covers key probability concepts such as dependent events and includes a step-by-step breakdown. Suitable for students in Grades 6-8.

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