Question

The probability that someone has gone to grad school is 0.30. Given that someone went to grad school, the probability that they work in their field of study is 0.75. The probability that they went to grad school or work in their field of study is 0.65. What is the probability that someone works in their field of study?

Answer 1

P(work in field of study) = 0.575

Explanation:

We are given;

P(went to grad school) = 0.3

P(went to grad school | work in field of study) = 0.75

P(went to grad school or work in field of study) = 0.65

Now, to find the probability that someone works in their field of study is gotten by the relationship;

P(went to grad school or work in field of study) = P(went to grad school) + P(work in field of study) - P(went to grad school and work in field of study)

Now, from the probability formula of;

P(A ∩ B) = P(A) × P(A | B), we have;

P(went to grad school and work in field of study) = P(went to grad school) × P(went to grad school | work in field of study)

Thus;

P(went to grad school and work in field of study) = 0.3 × 0.75 = 0.225

Plugging in the relevant values gives;

0.65 = 0.3 + P(work in field of study) - 0.225

P(work in field of study) = 0.65 + 0.225 - 0.3

P(work in field of study) = 0.575