There are three colored cookie jars. One jar is blue, another green and the last

Question

There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 15 chocolate chip and 9 sugar cookies. The green jar contains 6 chocolate chip, 11 sugar and 10 peanut butter cookies. The pink jar contains 5 chocolate chip, 7 sugar and 14 peanut butter cookies. One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are 12 , 14 , and 14 , respectively. A cookie is then chosen at random from the chosen jar. What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie?

a) 0.2692

b) 0.1887

c) 0.0897

d) 0.0673

e) 0.2560

Explanation / Answer

P(Pink jar was chosen|cookie was a sugar cookie)

P(cookie was a sugar cookie) = 1/2*(9/24)+(1/4)*(11/27)+(1/4)*(7/26) = 0.35666

P(Pink jar was chosen|cookie was a sugar cookie) = (1/4)*(7/26)/0.35666= 0.1887

Option B is Correct

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