Probability

For two events $A$ and $B$, it is given that $P(A)=P\left(\frac{A}{B}\right)=\frac{1}{4}$ and $P\left(\frac{B}{A}\right)=\frac{1}{2}$. Then

If $P(n): 1+3+5+\ldots+(2 n-1)=n^2$ is

Probability of getting a total of 7 or 9 in a single throw of two dice is

One mapping (function) is selected at random from all the mappings of the set $A=\{1,2,3, \ldots, n\} \quad$ into itself. The probability that the mapping selected is one-one, is

If $x$ follows a binomial distribution with parameters $n=100$ and $p=\frac{1}{3}$, then $p(X=r)$ is maximum when $r$ equals

In a trial, the probability of success is twice the probability of failure. In six trial, the probability of atleast four successes will be

If $x$ follows a binomial distribution with parameters $n=100$ and $p=\frac{1}{3}$, then $p(X=r)$ is maximum when $r$ equals

If $A$ and $B$ are two such events that $P(A \cup B)^{\prime}=P(A \cap B)$, then which of the following is true?

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for complement of event $A$. Then, the events $A$ and $B$ are

If $X$ follows a binomial distribution with parameters $n=8$ and $p=\frac{1}{2}$, then $P(|x-4| \leq 2)$ is equal to

Out of 50 tickets numbered $00,01,02, \ldots, 49$, one ticket is drawn randomly, the probability of the ticket having the product of its digits 7 , given that the sum of the digits is 8 , is

A multiple choice examination has 5 questions. Each question has 4 alternative answer of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing is