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 6 brown marbles and 8 clear marbles. Urn 2 contains 15 brown marbles, 12 clear marbles and 11 red marbles. Urn 3 contains 13 brown marbles, 7 clear marbles and 5 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) 0.2399

b) 0.0933

c) 0.2800

d) 0.0700

e) 0.1610

Explanation / Answer

Probability of choosing an urn3 = 1/4 Total Number of marbles in urn3 = 25 Number of Clear marbles in urn 3 = 7 Probability of clear marble in urn 3 = 7/25 Probability that urn 3 was chosen and marble chosen was clear = (1/4)*(7/25) = 0.07 Solution Option D

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