$A$ coin is tossed three times. If event $E$ represents getting at least two heads and event $F$ represents getting a head on the first toss,find $P(E|F)$.

Let $E$ and $F$ be events with $P(E)=\frac{3}{5}, P(F)=\frac{3}{10}$ and $P(E \cap F)=\frac{1}{5}$. Are $E$ and $F$ independent?

Two cards are drawn one by one from a pack of cards. The probability of getting the first card as an ace and the second as a coloured card is (without replacement).

If $A$ and $B$ are two events such that $P(A)=\frac{1}{2}$,$P(B)=\frac{1}{2}$ and $P(A \mid B)=\frac{1}{4}$,then $P(A^{\prime} \cap B^{\prime})$ is

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl?

Three numbers are chosen at random without replacement from $\{1, 2, 3, 4, 5, 6, 7, 8\}$. The probability that their minimum is $3$,given that their maximum is $6$,is: