Final answer:
The probability that Eduardo selects a chocolate chip cookie and then a peanut butter cookie is 8%, calculated by multiplying the probability of each individual selection (8/25 for chocolate chip and 6/24 for peanut butter after eating a chocolate chip).
Step-by-step explanation:
The question involves calculating the probability of a compound event, where Eduardo selects one chocolate chip cookie and then a peanut butter cookie. To solve this, we must consider the sequence of two events.
Calculating the Probability of Selecting a Chocolate Chip Cookie
First, let's find the probability that Eduardo selects a chocolate chip cookie on his first try. The total number of cookies in the bag is 8 (chocolate chip) + 6 (peanut butter) + 4 (sugar) + 7 (oatmeal) = 25 cookies.
The probability of selecting a chocolate chip cookie is therefore the number of chocolate chip cookies divided by the total number of cookies: P(Chocolate chip) = 8/25.
Calculating the Probability of Selecting a Peanut Butter Cookie After Eating a Chocolate Chip Cookie
Next, we have to calculate the probability of Eduardo selecting the peanut butter cookie after having already eaten a chocolate chip cookie. Now the total number of cookies is one less, because Eduardo ate one, so there are 24 cookies left.
The number of peanut butter cookies hasn't changed, so the probability of selecting a peanut butter cookie now is P(Peanut butter after Chocolate chip) = 6/24.
Compound Probability of Both Selections
To find the total probability of both selections, we multiply the probability of the first event by the probability of the second event, assuming the first event has occurred.
So the probability of first selecting a chocolate chip cookie and then a peanut butter cookie is P(Chocolate chip and Peanut butter) = P(Chocolate chip) * P(Peanut butter after Chocolate chip) = (8/25) * (6/24).
Therefore, the compound probability is (8/25) * (6/24) = 48/600
= 0.08,
which after simplification gives us a final probability of 0.08 or 8%.