In a certain population $10\%$ of the people are rich, $5\%$ are famous and $3\%$ are 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
$0. 07$
$0.08$
$0. 09$
$0. 12$
If $P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7$ and the events $A$ and $B$ are mutually exclusive, then $x = $
If $A$ and $B$ are two independent events, then $A$ and $\bar B$ are
If $A$ and $B$ are any two events, then the probability that exactly one of them occur is
If $P(A) = \frac{1}{2},\,\,P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{7}{{12}},$ then the value of $P\,(A' \cap B')$ is
In a horse race the odds in favour of three horses are $1:2 , 1:3$ and $1:4$. The probability that one of the horse will win the race is