Question

According to the Stack Overflow Developers Survey of 20184, 25.8% of developers are students.The probability that a developer is a woman given that the developer is a student is 7.4%,and the probability that a developer is a woman given that the developer is not a student is76.4%. If we encounter a woman developer, what is the probability that she is a student

Answer 1

0.0326 = 3.26% probability that she is a student.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Woman developer

Event B: Student

Probability that the developer is a woman:

7.4% of 25.8%(students).

76.4% of 100 - 25.8 = 74.2%(not students). So

`P(A) = 0.074*0.258 + 0.764*0.742 = 0.58598`

Student and woman developer.

7.4% of 25.8%(students), so

`P(A \cap B) = 0.074*0.258 = 0.019092`

If we encounter a woman developer, what is the probability that she is a student

`P(B|A) = (P(A \cap B))/(P(A)) = (0.019092)/(0.58598) = 0.0326`

0.0326 = 3.26% probability that she is a student.