An experiment consists of choosing an urn with the following probabilities that

Question

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 7 clear marbles. Urn 2 contains 15 brown marbles, 9 clear marbles and 8 red marbles. Urn 3 contains 11 brown marbles, 5 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) 0.1724

b) 0.0575

c) 0.1350

d) 0.0431

e) 0.1992

Explanation / Answer

The correct option is C

Explanation:

P(clear) = sum of P(urn #) * P(clear | urn #)

P(clear) = 1/2 (7 / 17) + 1/4 (9 / 32) + 1/4 (5 / 29)
P(clear) =7 / 34 + 9/ 128 + 5 / 116
P(clear) = 0.2058 + 0.0703 + 0.0431 =0.3192

of this total probability of a clear marble, 1/4 (5/29) = 5/116 = 0.043 comes from urn 3

so P(urn 3 | clear) = (0.043) / (0.3192) = 0.13499

P(urn 3 | clear) = .1350

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