$A$ 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

$A$ box contains $6$ nails and $10$ nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random,what is the probability that it is rusted or is a nail?

$A, B, C$ are aiming to shoot a balloon. $A$ will succeed $4$ times out of $6$ attempts. The chance of $B$ to shoot the balloon is $3$ out of $5$ and that of $C$ is $2$ out of $3$. If the three aim to shoot the balloon simultaneously,then the probability that at least two of them hit the balloon is

Three coins are tossed simultaneously. Consider the events $E$: 'three heads or three tails',$F$: 'at least two heads',and $G$: 'at most two heads'. Of the pairs $(E, F)$,$(E, G)$,and $(F, G)$,which are independent and which are dependent?

If two different numbers are taken from the set $\{0, 1, 2, 3, \dots, 10\}$,then the probability that their sum as well as their absolute difference are both multiples of $4$ is:

$A$ bag contains $3$ white,$2$ blue,and $5$ red balls. One ball is drawn at random from this bag. The probability that the ball drawn is not red is