Question

In a neighborhood 60% of the houses have a garage and a fenced in backyard. Given that 80% of the houses in the neighborhood have a garage, what is the probability that a house has a fenced in backyard given that it has a garage?
A) 20%
B) 48%
C) 75%
D) 80%

Answer 1

The correct answer will be 75 for anyone wondering

Answer 2

Answer:  C) 75%

Step-by-step explanation:

Let G represents the event of having garbage in houses and F represents the event of houses having fenced in backyard.

Given: In neighborhood , the probability of houses have a garage and a fenced in backyard $P(G\cap F)= 60\%=0.6$

The probability of houses have a garage P(G)=80%=0.8

The probability that a house has a fenced in backyard given that it has a garage is given by :-

$P(F|G)=\dfrac{P(G\cap F)}{P(G)}\\\\\Rightarrow\ P(F|G)=\dfrac{0.6}{0.8}=0.75$

In percent, $0.75\times100=75\%$

Hence, the probability that a house has a fenced in backyard given that it has a garage = 75%.