In a neighborhood 60% of the houses have a garage and a fenced in backyard. Given that 80% of the houses in the neighborhood hav

Question

3 years ago

11

e 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%

2 answers:

Tpy6a [65] · Answer 1 · 2022-05-15T05:05:17+03:00

Tpy6a [65]3 years ago

8 0

The correct answer will be 75 for anyone wondering

xxMikexx [17] · Answer 2 · 2022-05-15T06:15:14+03:00

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%.