Answered

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Warren buys a bag of cookies that contains 5 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cookies.What is the probability that Warren reaches in the bag and randomly selects 2 peanut butter cookies from the bag? Round your answer to four decimal places. Hint: Did you use conditional probability?

Sagot :

ANSWER

0.0593

EXPLANATION

The total number of cookies in the bag is,

[tex]5+6+6+6=23[/tex]

When Warren takes the first cookie, the probability of it being a peanut butter cookie is 6 out of 23,

[tex]P(pb_1)=\frac{6}{23}[/tex]

If the first cookie was peanut butter, when he takes the second cookie there are only 5 peanut butter cookies left and a total of 22 cookies, so the probability of that second cookie being peanut butter is,

[tex]P(pb_2)=\frac{5}{22}[/tex]

So, the probability that Warren selects 2 peanut butter cookies from the bag is,

[tex]P(2pb)=\frac{6}{23}\times\frac{5}{22}\approx0.0593[/tex]

Hence, the probability that he takes 2 peanut butter cookies is 0.0593.

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