Given $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$. Find $P(A \text{ or } B)$,if $A$ and $B$ are mutually exclusive events.

The odds against a certain event is $5 : 2$ and the odds in favour of another event is $6 : 5$. If both the events are independent,then the probability that at least one of the events will happen is

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,then the value of $P(A \cup B)$ is

The probability that a student will succeed in the $IIT$ entrance test is $0.2$ and the probability that he will succeed in the Roorkee entrance test is $0.5$. If the probability that he will be successful at both places is $0.3$,then the probability that he does not succeed at either place is:

If ${A_1}, {A_2}, ..., {A_n}$ are any $n$ events,then: