The probability of selecting a chocolate chip cookie on the first draw is 5/24, since there are 5 chocolate chip cookies in the bag out of a total of 24 cookies. After eating the chocolate chip cookie, there are 23 cookies left in the bag, including 5 peanut butter cookies. So the probability of selecting a peanut butter cookie on the second draw is 5/23.
To find the probability of both events happening, we multiply the probabilities:
P(select chocolate chip then peanut butter) = P(select chocolate chip) × P(select peanut butter after selecting chocolate chip)
= (5/24) × (5/23)
We can reduce this fraction by finding the greatest common factor of the numerator and denominator, which is 1 in this case:
P(select chocolate chip then peanut butter) = (5/24) × (5/23) = 25/1104
Therefore, the probability that Alan randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a peanut butter cookie is 25/1104.