Question

Number of Children

Salary 2 or fewer children more than 2 children

high salary 0.13 0.02

medium salary 0.20 0.10

low salary   0.30 0.25

Let A denote the event that a working woman has 2 or fewer children, and let B denote the event that a working woman has a low salary.

a. If a working woman has 2 or fewer children, what is the probability that she has a low salary?

b. What is the probability that a working woman has 2 or fewer children or has a low salary?

Answer 1

We are given here that:
A: woman has <= 2 children
B: woman has low salary

a) Probability that the woman has low salary given that woman has <= 2 children is denoted as: P(B|A)
This is computed using bayes theorem as:

Therefore 0.4762 is the required probability here.

b) The probability here is computed using the addition law of probability as:

Therefore 0.88 is the required probability here.