Question

In a certain town, $60\%$ of the families own a car, $30\%$ own a house and $20\%$ own both car and house. If a family is randomly chosen, then 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 $0.5$

Let $A$ be the set of families who own a car and $B$ be the set of families who own a house.
Then,

$P\left(A\right)=60\%,P\left(B\right)=30\%$
and

$P(A\cap B)=20\%$

Now,

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=60+30-20=70\%$

Now, families who owns a car or a house but not both $=A\Delta B$
$\Rightarrow P\left(A\Delta B\right)=P(A\cup B)-P(A\cap B)$
$=70-20=50\%=0.5$