If $A$ and $B$ are any two events, then the probability that exactly one of them occur is
$P\,(A) + P\,(B) - P\,(A \cap B)$
$P\,(A) + P\,(B) - 2P\,(A \cap B)$
$P\,(A) + P\,(B) - P\,(A \cup B)$
$P\,(A) + P\,(B) - 2P\,(A \cup B)$
A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is
Three persons $P, Q$ and $R$ independently try to hit a target . If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $P$ or $Q$ but not by $R$ is
In a class of $125$ students $70$ passed in Mathematics, $55$ in Statistics and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is
If $P(A) = P(B) = x$ and $P(A \cap B) = P(A' \cap B') = \frac{1}{3}$, then $x = $
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