Walter buys a bag of cookies that contains 5 chocolate chip cookies, 6 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies. what is the probability that walter randomly selects an oatmeal cookie from the bag, eats it, then randomly selects a peanut butter cookie?
The total number of cookies in the bag is 5 + 6 + 8 + 8 = 27.
The probability of randomly selecting an oatmeal cookie from the bag is 8/27.
After eating the oatmeal cookie, there are now 26 cookies in the bag.
The probability of randomly selecting a peanut butter cookie from the remaining 26 cookies is 6/26.
Therefore, the probability that Walter randomly selects an oatmeal cookie and then a peanut butter cookie is (8/27) * (6/26) = 48/702 ≈ 0.06834 (rounded to five decimal places).
To find the probability, we need to calculate the total number of possible outcomes and the number of favorable outcomes.
Step 1: Calculate the total number of possible outcomes:
The total number of cookies in the bag = 5 chocolate chip + 6 peanut butter + 8 sugar + 8 oatmeal = 27 cookies
Walter can choose any cookie from these 27 cookies as the first choice.
Step 2: Calculate the number of favorable outcomes:
After Walter eats an oatmeal cookie, there will be 7 oatmeal cookies left in the bag. Now, Walter can choose any of these 7 oatmeal cookies.
Once he chooses an oatmeal cookie, there will be 5 chocolate chip cookies, 6 peanut butter cookies, 8 sugar cookies, and 7 oatmeal cookies remaining in the bag.
Now, Walter can choose any of the 6 peanut butter cookies from these remaining 26 cookies as his second choice.
Step 3: Calculate the probability:
The probability of randomly selecting an oatmeal cookie, eating it, and then randomly selecting a peanut butter cookie can be calculated as:
Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 7 (number of choices for the first oatmeal cookie) * 6 (number of choices for the second peanut butter cookie) = 42
Total number of possible outcomes = 27 (total number of cookies)
Probability = Number of favorable outcomes / Total number of possible outcomes = 42 / 27 ≈ 0.7778
Therefore, the probability that Walter randomly selects an oatmeal cookie from the bag, eats it, and then randomly selects a peanut butter cookie is approximately 0.7778 (or 77.78%).
To find the probability that Walter randomly selects an oatmeal cookie first and then randomly selects a peanut butter cookie, we need to know the total number of cookies and the number of oatmeal and peanut butter cookies.
Step 1: Find the total number of cookies in the bag.
The bag contains:
- 5 chocolate chip cookies
- 6 peanut butter cookies
- 8 sugar cookies
- 8 oatmeal cookies
To find the total number of cookies, add up all the different types of cookies:
Total number of cookies = 5 + 6 + 8 + 8 = 27 cookies
Step 2: Find the probability of selecting an oatmeal cookie first.
The probability of selecting an oatmeal cookie is the ratio of oatmeal cookies to the total number of cookies:
P(selecting an oatmeal cookie) = Number of oatmeal cookies / Total number of cookies
P(selecting an oatmeal cookie) = 8/27
Step 3: Find the probability of selecting a peanut butter cookie after eating the oatmeal cookie.
After eating the oatmeal cookie, there will be 26 cookies left in the bag.
Now, the bag contains:
- 5 chocolate chip cookies
- 6 peanut butter cookies
- 8 sugar cookies
- 7 oatmeal cookies
The probability of selecting a peanut butter cookie is the ratio of peanut butter cookies to the remaining number of cookies:
P(selecting a peanut butter cookie) = Number of peanut butter cookies / Remaining number of cookies
P(selecting a peanut butter cookie) = 6/26
Step 4: Find the probability of both events happening (selecting an oatmeal cookie first and a peanut butter cookie second).
The probability of both events happening is the product of the probabilities of each event:
P(both events happening) = P(selecting an oatmeal cookie) * P(selecting a peanut butter cookie)
P(both events happening) = (8/27) * (6/26)
P(both events happening) ≈ 0.067
Therefore, the probability that Walter randomly selects an oatmeal cookie from the bag, eats it, and then randomly selects a peanut butter cookie is approximately 0.067 or 6.7%.