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A jar contains 3 chocolate cookies, 5 peanut butter cookies, and 6 coconut cookies. If 3 cookies are selected in succession, what is the probability of selecting chocolate, then peanut butter, and then coconut cookies, if replacement occurs each time?

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JcAlmighty
The answer is 45/1372.

There are in total 14 cookies (3 chocolate cookies + 5 peanut butter cookies + 6 coconut cookies).
The probability of selecting chocolate cookies is the number of chocolate cookies divided by total number of cookies: 3/14
The probability of selecting peanut butter cookies is the number of peanut butter cookies divided by total number of cookies: 5/14
The probability of selecting coconut cookies is the number of coconut cookies divided by total number of cookies: 3/14

Since replacement occurs each time, that means that the total number of cookies remain the same. To calculate  the probability of selecting chocolate, then peanut butter, and then coconut cookies, we will use the multiplication rule which says that if events occur together, their probabilities multiply:
3/14 * 5/14 * 6/14 = (3*5*6)/(14*14*14) = 90/2744 = 45/1372

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