The probability that an event will fail to happen is $0.05$. The probability that the event will take place on $4$ consecutive occasions is

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively, then $P(X \geq 1)$ is equal to

Five cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. What is the probability that none is a spade?

$A$ random variable $X$ follows the binomial distribution and $X \sim B(n, 0.3)$. If the mean of $X$ is three times as large as the standard deviation of $X$,then $n=$

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting a head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$,respectively. Suppose $\alpha$ is the number of heads that appear when $C_1$ is tossed twice,independently,and $\beta$ is the number of heads that appear when $C_2$ is tossed twice,independently. Then,the probability that the roots of the quadratic polynomial $x^2 - \alpha x + \beta$ are real and equal is:

$A$ radar system can detect an enemy plane in one out of ten consecutive scans. The probability that it can detect an enemy plane at least twice in four consecutive scans is