Holly buys a bag of cookies that contains 4 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookiesand 8 oatmeal cookies.What is the probability that Holly reaches in the bag and randomly selects an oatmeal 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.

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ZanT132070 ZanT132070

03-11-2022
Mathematics

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Holly buys a bag of cookies that contains 4 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookiesand 8 oatmeal cookies.What is the probability that Holly reaches in the bag and randomly selects an oatmeal 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.

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CaylynE513595 CaylynE513595 · Answer 1 · 2022-11-03T00:23:33-04:00

The bag contains: 4 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies.

Therefore, there is a total of 24 cookies.

Thus, the probability of selecting an oatmeal cookie (8) from the bag (24) is: 1/3

[tex]P_1=\frac{8}{24}=\frac{1}{3}\approx0.3333\ldots[/tex]

After she eats this cookie, there are 23 cookies left.

Now, the probability of selecting a peanut butter cookie (4) from the bag (23) is: 4/23

[tex]P_2=\frac{4}{23}=0.17391\approx0.1739[/tex]

Now, the probability of these two events to happen, is the following: 4/69

[tex]\begin{gathered} P_{1\&2}=P_1\cdot P_2=\frac{8}{24}\cdot\frac{4}{23} \\ =\frac{1}{3}\cdot\frac{4}{23} \\ =\frac{4}{69} \\ \approx0.0580 \end{gathered}[/tex]

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