In a bag there are three tickets numbered $1, 2, 3$. $A$ ticket is drawn at random and put back,and this is done four times. The probability that the sum of the numbers is even is:

For any two events $A$ and $B$ in a sample space,which of the following is always true?

Let there be three independent events $E_{1}, E_{2}$ and $E_{3}$. The probability that only $E_{1}$ occurs is $\alpha$,only $E_{2}$ occurs is $\beta$ and only $E_{3}$ occurs is $\gamma$. Let $p$ denote the probability that none of the events occur,which satisfies the equations $(\alpha - 2\beta)p = \alpha\beta$ and $(\beta - 3\gamma)p = 2\beta\gamma$. All the given probabilities are assumed to lie in the interval $(0, 1)$. Then,$\frac{\text{Probability of occurrence of } E_{1}}{\text{Probability of occurrence of } E_{3}}$ is equal to ..........

In a single throw of three dice,the probability of getting a sum at least $5$ is

All face cards from a pack of $52$ playing cards are removed. From the remaining $40$ cards,two are drawn randomly without replacement. The probability of drawing a pair (cards of the same denomination) is:

If the probabilities of three independent events occurring are $p_1, p_2, p_3$,what is the probability that at least one of these events occurs?