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%

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)=(P(G\cap F))/(P(G))\\\\\Rightarrow\ P(F|G)=(0.6)/(0.8)=0.75`

In percent,
`0.75*100=75\%`

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