If $P(A \cup B) = \frac{2}{3}$,$P(A \cap B) = \frac{1}{6}$,and $P(A) = \frac{1}{3}$,then which of the following is true?

$A$ and $B$ are events such that $P(A)=0.42$,$P(B)=0.48$ and $P(A \cap B)=0.16$. Determine $P(A \cup B)$.

In a certain population,$10\%$ of the people are rich,$5\%$ are famous,and $3\%$ are both rich and famous. The probability that a person picked at random from the population is either famous or rich but not both,is equal to

The probability of occurrence of an event $A$ is $1/2$ and that of $B$ is $3/10$. If $A$ and $B$ are mutually exclusive, then the probability of occurrence of neither $A$ nor $B$ is (in $/5$)

$A$ and $B$ are two events such that $P(A)=0.54$,$P(B)=0.69$ and $P(A \cap B)=0.35$. Find $P(A \cup B)$.

The odds against a person who is $40$ years old living until he is $70$ are $8$ to $5$,and the odds against another person who is $50$ years old living until he is $80$ are $4$ to $3$. Find the probability that exactly one of them will be alive $30$ years from now.