51.3k views
1 vote
Alan buys a bag of cookies that contains 5 chocolate chip cookies, 5 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies. What is the probability that Alan randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a peanut butter cookie? Express you answer as a reduced fraction

User Xerq
by
8.4k points

1 Answer

3 votes
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.
User Robert Mikes
by
7.8k points