# Use Bayes Theorem to calculate the probabilities:The enrollment in a certain course is 10% first year students, 30% sophomores, 40% juniors and 20% seniors.  Past experience has shown that the likelihood of receiving an A in the course is .2 for first year students, .4 for sophomores, .3 for juniors and .1 for seniors.  Find the probability that a student who receives an A is a sophomore.

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Use Bayes Theorem to calculate the probabilities:

The enrollment in a certain course is 10% first year students, 30% sophomores, 40% juniors and 20% seniors.  Past experience has shown that the likelihood of receiving an A in the course is .2 for first year students, .4 for sophomores, .3 for juniors and .1 for seniors.  Find the probability that a student who receives an A is a sophomore.

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Step 1

Given

probability of first year students enrolment in course P(F) = 0.10

probability of sophmores enrolment in course P(S) = 0.30

probability of Seniors enrolment in course P(Sen) = 0.20

probability of Juniors enrolment in course P(J) = 0.40

probability of recieving A among first year students P(A | F) =0.20

probability of recieving A among sophomores  P(A | S) =0.40

probability of recieving A among Seniors  P(A | Sen) =0.10

probability of recieving A among Juniors  P(A | J) =0.30

Here from the conditional probability definition we calculate the following probabilities

Step 2

Total students = first year + Sophomores + Juniors + Seniors

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