Given that the events $A$ and $B$ are such that $P(A) = \frac{1}{2}$,$P(A \cup B) = \frac{3}{5}$,and $P(B) = p$. Find $p$ if they are mutually exclusive.

If $A$ and $B$ are mutually exclusive events,given that $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$,then $P(A \text{ or } B)$ is

Fill in the blanks in the following table:

$P(A)$	$P(B)$	$P(A \cap B)$	$P(A \cup B)$
$0.5$	$0.35$	$.........$	$0.7$

If the probability of a horse $A$ winning a race is $1/4$ and the probability of a horse $B$ winning the same race is $1/5$,then the probability that either of them will win the race is (in $/20$)

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

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.