There are two children in a family. The probability that both of them are boys is

Two brothers $X$ and $Y$ appeared for an exam. Let $A$ be the event that $X$ has passed the exam and $B$ is the event that $Y$ has passed. The probability of $A$ is $\frac{1}{7}$ and of $B$ is $\frac{2}{9}$. Then,the probability that both of them pass the exam is

$A$ die is thrown. Find the probability of the following event: $A$ number greater than or equal to $3$ will appear.

$A$ coin is tossed. If it shows head,we draw a ball from a bag consisting of $3$ blue and $4$ white balls; if it shows tail,we throw a die. Describe the sample space of this experiment.

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$,then which of the following is correct?

An anti-aircraft gun takes four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first,second,third,and fourth shots are $0.4, 0.3, 0.2$,and $0.1$ respectively. The probability that the gun hits the plane is: