Sunny buys a bag of cookies that contains 6 chocolate chip cookies, 4 peanut butter cookies, 5 sugar cookies and 6 oatmeal cookies. What is the probability that Sunny randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a sugar cookie? Express you answer as a reduced fraction.


We need to find the probability of two successive events:

1. The probability that Sunny selects a peanut butter cookie first.
2. The probability that Sunny selects a sugar cookie second, after eating the peanut butter cookie.

### Step 1: Calculate total number of cookies.
The total number of cookies in the bag is:
\[
6 \ (\text{chocolate chip}) + 4 \ (\text{peanut butter}) + 5 \ (\text{sugar}) + 6 \ (\text{oatmeal}) = 21 \ \text{cookies}.
\]

### Step 2: Find the probability of selecting a peanut butter cookie.
The number of peanut butter cookies is 4, so the probability of selecting a peanut butter cookie first is:
\[
\frac{4}{21}.
\]

### Step 3: Find the probability of selecting a sugar cookie after eating the peanut butter cookie.
After Sunny eats one peanut butter cookie, the total number of cookies left is \( 21 - 1 = 20 \). The number of sugar cookies remains 5, so the probability of selecting a sugar cookie next is:
\[
\frac{5}{20} = \frac{1}{4}.
\]

### Step 4: Multiply the probabilities of the two events.
The total probability of selecting a peanut butter cookie first and a sugar cookie second is:
\[
\frac{4}{21} \times \frac{1}{4} = \frac{4}{84} = \frac{1}{21}.
\]

Thus, the probability that Sunny selects a peanut butter cookie, eats it, and then selects a sugar cookie is \( \frac{1}{21} \).

Would you like further explanation or additional examples?

Here are 5 related questions:
1. What is the probability that Sunny selects two chocolate chip cookies in a row?
2. What is the probability that Sunny selects an oatmeal cookie first and then a sugar cookie?
3. How does the probability change if one more peanut butter cookie is added to the bag?
4. What is the probability that Sunny does not select a peanut butter cookie or a sugar cookie?
5. If Sunny selects three cookies, what is the probability they are all different types?

**Tip:** When dealing with successive events in probability, remember to adjust the total number of items after each selection if the items are not replaced.

Sunny buys a bag of cookies that contains 6 chocolate chip cookies, 4 peanut butter cookies, 5 sugar cookies and 6 oatmeal cookies. What is the probability that Sunny randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a sugar cookie? Express your answer as a reduced fraction.

Learn how to calculate the probability that Sunny selects a peanut butter cookie, eats it, and then selects a sugar cookie from a bag containing 6 chocolate chip cookies, 4 peanut butter cookies, 5 sugar cookies, and 6 oatmeal cookies. This problem explores dependent events and the multiplication rule. Suitable for students in Grades 6-8.

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