$A$ 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?

$A$ student appears for tests $I$, $II$, and $III$. The student is successful if they pass in tests ($I$ and $II$) $OR$ ($I$ and $III$). The probabilities of the student passing in tests $I$, $II$, and $III$ are respectively $p$, $q$, and $1/2$. If the probability of the student being successful is $1/2$, then:

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}$ respectively. The probability that neither of them wins the race is:

When two dice are thrown,the probability of getting the sum of the values on them as $10$ or $11$ is

In a single throw of a fair die,what is the probability of getting a number less than $7$?

What is the probability of getting at least one tail when a coin is tossed $4$ times?