If the odds against an event be $2 : 3$,then the probability of its occurrence is

For any two events $A$ and $B$,if $P(A \cup B) = a P(A \cap B) + b P(A) + c P(B)$,then $3a + 2b + 5c = ?$

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 they will be studying Mathematics or Biology.

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:

$P(A)$	$P(B)$	$P(A \cap B)$	$P(A \cup B)$
$\frac{1}{3}$	$\frac{1}{5}$	$\frac{1}{15}$	$........$

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