India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0, 1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is

From the employees of a company, $5$ persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows :

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over $35$ years?

If $A$ and $B$ are two events such that $P\,(A \cup B)\, + P\,(A \cap B) = \frac{7}{8}$ and $P\,(A) = 2\,P\,(B),$ then $P\,(A) = $

An event has odds in favour $4 : 5$, then the probability that event occurs, is

If $A$ and $B$ are two independent events, then the probability of occurrence of at least one of $\mathrm{A}$ and $\mathrm{B}$ is given by $1 -\mathrm{P}\left(\mathrm{A}^{\prime}\right) \mathrm{P}\left(\mathrm{B}^{\prime}\right)$

$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P \left( A \cap B ^{\prime}\right)$ .