Question

In a city, 60% of the residents live in houses and 40% of the residents live in apartments.Of the people who live in houses, 20% own their own business. Of the people who live in apartments, 10% own their own business.
1. If a person owns his or her own business, find the probability that he or she lives in a house.

Answer 1

Answer:

0.75 or 75%

Step-by-step explanation:

The probability that a resident lives in a house and owns their own business is:

$P(H\cap B)=0.6*0.2\\P(H\cap B)=0.12$

The probability that a resident lives in an apartment and owns their own business is:

$P(A\cap B)=0.4*0.1\\P(A\cap B)=0.04$

Therefore, the probability that a person lives in a house, given that they own their own business is:

$P(H|B) = \frac{P(H\cap B)}{P(H\cap B)+P(A\cap B)}\\P(H|B) = \frac{0.12}{0.12+0.04} \\P(H|B) = 0.75$

The probability is 0.75 or 75%.