29) A student enrolls in a statistics class. There is a probability of 0.6 that

Question

29) A student enrolls in a statistics class. There is a probability of 0.6 that they will be assigned to Professor Jones’s class, and a probability of 0.4 that they will be assigned to Professor Smith. Historically the probability of getting a B or higher in Professor Jones’s class was 0.7 while in Professor Smith’s class it was 0.9. What is the probability that the student will get a B or better?

Using the same data as Question 29 answer the following question. Given that a student achieved less than a B, what is the probability that the student had Professor Smith as an instructor?

Explanation / Answer

29.

Let

J = Jones
S = Smith
B = got B or better

Hence, by Bayes' Rule,

P(B) = P(J) P(B|J) + P(S) P(B|S)

= 0.6*0.7 + 0.4*0.9

= 0.78 [ANSWER]

***********************************

b)

Hence,

P(B') = 1 - P(B) = 0.22

Thus,

P(S|B') = P(S) P(B'|S) / P(B')

= 0.4*(1-0.9)/0.22

= 0.181818182 [ANSWER]

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