Question

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

Answer 1

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