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One of two small classrooms is chosen at random with equally likely probability, and then a...

One of two small classrooms is chosen at random with equally likely probability, and then a student is chosen at random from the chosen classroom. Classroom #1 has 5 boys and 13 girls. Classroom #2 has 15 boys and 9 girls. What is the probability that Classroom #2 was chosen at random, given that a girl was chosen? Your answers should be rounded to 4 digits after the decimal.

A 0.6582

B 0.3418

C 0.1875

D 0.3750

E 0.2708

F None of the above

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Answer #1

P(girl) = P(girl | classroom 1) * P(classroom 1) + P(girl | classroom 2) * P(classroom 2)

          = (13/18) * (1/2) + (9/24) * (1/2)

          = 0.5486

P(classroom 2 | girl) = P(girl | classroom 2) * P(classroom 2) / P(girl) = (9/24) * (1/2) / 0.5486 = 0.3418

Option-B) 0.3418

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