$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is $3$.

In a lottery containing $35$ tickets,exactly $10$ tickets bear a prize. If a ticket is drawn at random,then the probability of not getting a prize is

Let $A$ and $B$ be two independent events of a random experiment. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$,then the probability of occurrence of $A$ is

$A$ problem is given to $3$ students $A, B$ and $C$ whose chances of solving it are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Then,the probability of the problem being solved by exactly one of them,if all the three try independently,is

The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then: