In class $XI$ of a school $40\%$ of the students study Mathematics and $30 \%$ study Biology. $10 \%$ of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
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
For two given events $A$ and $B$, $P\,(A \cap B) = $
Let $A$ and $B$ be events for which $P(A) = x$, $P(B) = y,$$P(A \cap B) = z,$ then $P(\bar A \cap B)$ equals
One card is drawn from a pack of $52$ cards. The probability that it is a queen or heart is