Ashton buys a bag of cookies that contains 6 chocolate chip cookies, 4 peanut butter cookies, 7 sugar cookies and 8 oatmeal cookies. What is the probability that Ashton reaches in the bag and randomly selects 2 peanut butter cookies from the bag? Round your answer to four decimal places.
Question
Ashton buys a bag of cookies that contains 6 chocolate chip cookies, 4 peanut butter cookies, 7 sugar cookies and 8 oatmeal cookies.
What is the probability that Ashton reaches in the bag and randomly selects 2 peanut butter cookies from the bag? Round your answer to four decimal places.
Solution
To solve this problem, we first need to determine the total number of cookies in the bag.
Ashton has:
- 6 chocolate chip cookies
- 4 peanut butter cookies
- 7 sugar cookies
- 8 oatmeal cookies
So, the total number of cookies in the bag is 6 + 4 + 7 + 8 = 25 cookies.
The probability of selecting a peanut butter cookie on the first draw is 4 (the number of peanut butter cookies) divided by 25 (the total number of cookies), which equals 0.16.
After one peanut butter cookie has been drawn, there are now 3 peanut butter cookies left and 24 total cookies left in the bag. So, the probability of drawing a second peanut butter cookie is 3/24 = 0.125.
The probability of both events happening (drawing two peanut butter cookies in a row) is the product of the probabilities of each event. So, the probability that Ashton reaches in the bag and randomly selects 2 peanut butter cookies from the bag is 0.16 * 0.125 = 0.02.
Rounding to four decimal places, the probability is 0.0200.
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