Question

jonathan buys a bag of cookies that contains 4 chocolate chip cookies, 8 peanut butter cookies, 7 sugar cookies and 4 oatmeal cookies.
what is the probability that jonathan 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?
give your answer as a fraction, or accurate to at least 4 decimal places.
question help: video

Explanation:

Step1: Calculate the total number of cookies

The total number of cookies is $4 + 8+7 + 4=23$.

Step2: Calculate the probability of selecting a sugar cookie first

The probability of selecting a sugar cookie is $P(\text{sugar})=\frac{7}{23}$.

Step3: Calculate the number of remaining cookies

After eating a sugar cookie, the number of remaining cookies is $23 - 1=22$.

Step4: Calculate the probability of selecting a peanut - butter cookie second

The probability of selecting a peanut - butter cookie is $P(\text{peanut - butter})=\frac{8}{22}=\frac{4}{11}$.

Step5: Calculate the combined probability

Since these are independent events (the first event affects the sample space for the second event), we use the multiplication rule for probability. $P = P(\text{sugar})\times P(\text{peanut - butter})=\frac{7}{23}\times\frac{4}{11}=\frac{28}{253}=\frac{14}{255}\approx0.0549$.

Answer:

$\frac{14}{255}\approx0.0549$