$A$ die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of $4$. Then the conditional probability that the score $4$ has appeared at least once is

An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails } | \text{ } B \text{ has failed})$.

Let $A$ and $B$ be two events such that $P(A) = \frac{5}{11}$, $P(B) = \frac{2}{11}$, and $P(A \cup B) = \frac{3}{11}$, then $P(A'|B')$ is . . . . . . .

If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$,then which of the following is true?

Three coins are tossed. If one of them shows tail,then the probability that all three coins show tail,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 at least one is a girl?