If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

$A$ coin is tossed until a head appears or it has been tossed thrice. Given that a head does not appear on the first toss,what is the probability that the coin is tossed thrice?

Two planes $I$ and $II$ drop bombs on a target. The probabilities of hitting the target by $I$ and $II$ are $0.3$ and $0.2$ respectively. The second plane drops the bomb only if the first plane fails to hit the target. What is the probability that the second plane hits the target?

An urn $A$ contains $3$ white and $5$ black balls. Another urn $B$ contains $6$ white and $8$ black balls. $A$ ball is picked from $A$ at random and then transferred to $B$. Then, a ball is picked at random from $B$. The probability that it is a white ball is

Prove that if $E$ and $F$ are independent events,then so are the events $E$ and $F^{\prime}$.

If a die is rolled twice and the sum of the numbers appearing on them is observed to be $6$, then the probability that the number $1$ appears at least once on them is