The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$, then $P(A') + P(B')$ is

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

The number of $3$-digit numbers that are divisible by either $3$ or $4$ but not divisible by $48$ is:

If $U$ is the universal set with $100$ elements; $A$ and $B$ are two sets such that $n(A)=50$,$n(B)=60$,and $n(A \cap B)=20$,then find $n(A^{\prime} \cap B^{\prime})$.

Let $A = \{ x \in R : | x + 1 | < 2 \}$ and $B = \{ x \in R : | x - 1 | \geq 2 \}$. Then which one of the following statements is $NOT$ true?

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?