$A$ 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?

$5$ persons $A, B, C, D$ and $E$ are in a queue at a shop. The probability that $A$ and $E$ are always together is:

The probability of an event $A$ occurring is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,find the probability that neither $A$ nor $B$ occurs.

In a single throw of $3$ dice,find the probability of getting a total of at most $5$.

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is ${P_1}$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is ${P_2}$. Then:

There are $10$ pairs of shoes in a cupboard from which $4$ shoes are picked at random. The probability that there is at least one pair is