Three coins are tossed. Describe Two events which are mutually exclusive.

The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is

If a dice is thrown twice, then the probability of getting $1$ in the first throw only is

Let two fair dices $A$ and $B$ are thrown. Then the probability that number appears on dice $A$ is greater than number appears on dice $B$ is

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $