A problem of mathematics is given to three students whose chances of solving the problem are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$ respectively. The probability that the question will be solved is

$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P ( A \cup B )$.

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A$ and $B$ are mutually exclusive and exhaustive

Three fair coins are tossed. If both heads and tails appears, then the probability that exactly one head appears, is

The probability of choosing at random a number that is divisible by $6$ or $8$ from among $1$ to $90$ is equal to

Two dice are thrown. The events $A, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

Describe the events $A^{\prime }.$