Question

kele buys a bag of cookies that contains 8 chocolate chip cookies, 5 peanut butter cookies, 4 sugar cookies, and 7 oatmeal cookies. what is the probability that kele reaches in the bag and randomly selects a sugar cookie from the bag, eats it, then reaches back in the bag and randomly selects a peanut butter cookie? round your answer to four decimal places. question help: video

Explanation:

Step1: Calculate total number of cookies

Total number of cookies = 8 + 5+4 + 7=24.

Step2: Calculate probability of first - selecting a sugar cookie

The probability of selecting a sugar cookie first is $P_1=\frac{4}{24}=\frac{1}{6}$.

Step3: Calculate probability of second - selecting a peanut butter cookie

After eating one sugar cookie, there are 23 cookies left. The probability of selecting a peanut butter cookie second is $P_2=\frac{5}{23}$.

Step4: Calculate the combined probability

Since these are independent - like (sequential) events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{6}\times\frac{5}{23}=\frac{5}{138}\approx0.0362$.

Answer:

0.0362