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

Two dice are thrown together. The probability that at least one will show its digit $6$ is

In the random experiment of tossing two unbiased dice, let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?

The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins) is:

$A$ special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. $100$ $III$ year,$150$ $II$ year,and $200$ $I$ year students have applied for the room. Each $III$ year student's name is placed in the lottery $3$ times,each $II$ year student's name $2$ times,and each $I$ year student's name $1$ time. The probability that a $III$ year student gets the room is:

If $A$ and $B$ are two events,what is the probability that exactly one of them occurs?