23. Solve the following: 23a. There are three colored cookie jars. One jar is bl

Question

23. Solve the following:

23a.

There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 10 chocolate chip and 7 sugar cookies. The green jar contains 8 chocolate chip, 14 sugar and 11 peanut butter cookies. The pink jar contains 6 chocolate chip, 5 sugar and 9 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) 0.0833

b) 0.2302

c) 0.0625

d) 0.1669

e) 0.2500

f) None of the above.

23b.

An experiment consists of choosing an urn with the following probabilities that Urn 1, Urn 2, or Urn 3 will be chosen: 1/2, 1/4, and 1/4, respectively. Urn 1 contains 10 brown marbles and 8 clear marbles. Urn 2 contains 5 brown marbles, 11 clear marbles and 6 red marbles. Urn 3 contains 14 brown marbles, 9 clear marbles and 13 red marbles.   

A marble is then chosen from the chosen urn. What is the probability that Urn 3 was chosen, given that the marble chosen was clear?

a) 0.2093

b) 0.0625

c) 0.0833

d) 0.1525

e) 0.2500

f) None of the above.

Explanation / Answer

probability of Sugar cookie=P(blue jar and sugar cookie+green jar and sugar cookie+pink jar and sugar cookie)

=(1/2)*(7/17)+(1/4)*(14/33)+(1/4)*(5/20)=0.3744

therefore probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie

=P(pink jar and sugar cookie)/P(of Sugar cookie) =(1/4)*(5/20)/0.3744=0.1669

option D

23b)

P( clear marble)=P(Urn1 and clear marble+Urn2 and clear marble+Urn3 and clear marble)

=(1/2)*(8/18)+(1/4)*(11/22)+(1/4)*(9/36)=0.4097

therefore probability that Urn 3 was chosen, given that the marble chosen was clear

=P(Urn3 and clear marble)/P(clear marble) =(1/4)*(9/36)/0.4097 =0.1525

option D

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