The probability that an event $A$ happens in a trial is $0.4$. If three independent trials are made,then the probability that $A$ happens at least once is

Let $X \sim B(n, p)$. If $E(X)=5$ and $\operatorname{Var}(X)=2.5$,then find $P(X < 1)$.

Two dice are thrown simultaneously. If $X$ denotes the number of sixes,then the expectation of $X$ is

In a multiple-choice test consisting of $8$ questions,each question has four options. For each of the questions,exactly one of the four options is the right answer. $A$ student answers all the questions by choosing one option for each question. The number of ways in which the student can get exactly $5$ correct answers is

Four fair dice are thrown independently $27$ times. Then the expected number of times,at least two dice show up a three or a five,is

Two dice are thrown $4$ times simultaneously. What is the probability that both dice show the same numbers exactly twice?