The probability that Paulo randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a chocolate chip cookie is 18/253
How to find the probability
The probability of two independent events occurring in sequence is found by multiplying the probabilities of each event.
Let's denote the events:
P1: The event of randomly selecting a peanut butter cookie.
P2: The event of randomly selecting a chocolate chip cookie after selecting a peanut butter cookie.
Given that there are 6 peanut butter cookies in a total of
= 6 + 6 + 7 + 4 = 23 cookies
The probability of selecting a peanut butter cookie is 6/23.
After selecting a peanut butter cookie, there are now 22 cookies left (since one was already selected), and there are 6 chocolate chip cookies.
Therefore, the probability of selecting a chocolate chip cookie given that a peanut butter cookie was already selected is 6/22
Now, multiply the probabilities:
= 6 / 23 * 6 /22
= 18 / 253 as a reduced fraction