Question

In a certain town , $60$% of the families own a car, $30$% own a house and $20$% own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?

• A. $0.5$
• B. $0.7$
• C. $0.1$
• D. $0.9$

Answer 1

The correct option is A $0.5$

Probability that the family owns a car is $P\left(A\right)=0.6$
Probability that the family owns a house is $P\left(B\right)=0.3$
Probability that the family owns both a house and a car is $P(A\cap B)=0.2$

$\therefore$ The probability that the family owns a car or a house but not both is
$P(A\cup B)-P(A\cap B)=0.6+0.3-0.2-0.2=0.5$
Thus, the probability that this family owns a car or a house but not both is $0.5$.