Question

In: Statistics and Probability

Suppose that the probability that any random student graduates with honors is 0.07. Also, we know...

Suppose that the probability that any random student graduates with honors is 0.07. Also, we know that the probability of a student getting into grad school, given that they graduated with honors is 0.70. The probability of a student getting into grad school, given that they did not graduate with honors is 0.05. What is the probability that a student did not graduate with honors, given that the student did get in to graduate school?

A. 0.0514

B. 0.487

C. 0.513

D. 0.75

Solutions

Expert Solution

Solution:

Let

H =  student graduates with honors and NH =  student did not graduates with honors

the probability that any random student graduates with honors is 0.07.

thus

P(H) =0.07

thenP(NH ) =1 -P(H) = 1 - 0.07 = 0.93

Let G = a student getting into grad school,

the probability of a student getting into grad school, given that they graduated with honors is 0.70.

thus we have:

P(G|H) =0.70

and

The probability of a student getting into grad school, given that they did not graduate with honors is 0.05.

P(G|NH) =0.05

We have to find:
P( a student did not graduate with honors given  that the student did get in to graduate school) =............?

P(NH | G) =........?

Using Bayes rule:

Thus correct answer is: B. 0.487


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