Question

You are looking for a great person to spend your life with. The prior probability that someone is a great match is 0.1 (and I’m being generous here). If the person is a great match, their probability of having a good job is 0.8, whereas 30% of people who are not a great match also have a good job. On the first date you learn that the person has a good job.

What is the probability that they are a great match?

A. 0.2

B. 0.34

C. 0

D. 0.1

E. 0.23

Answer 1

E. 0.23

Explanation:

given that you are looking for a great person to spend your life with.

The prior probability that someone is a great matchi.e. event A is 0.1

Their probability of having a good job is 0.8,i.e. P(B/A)

whereas 30% of people who are not a great match also have a good job.

P(B/A')

On the first date you learn that the person has a good job.

Required probability = the probability that they are a great match/the person has a good job

=P(A/B) =
`(P(AB))/(P(B)) \\=(P(AB))/(P(AB)+P(A'B))`

since A and A' are mutually exclusive and exhaustive.

=
`(0.1*0.8)/(0.1*0.8+0.3*0.9) \\=(0.08)/(0.35) \\=0.2286`

After rounding off we find that

answre is option E) 0.23