Probability practice · Easy

Four tickets are marked 00,01, 10 and 11 respectively, are placed in a bag. A ticket is drawn at random five times, being replaced each time. The probability that the sum of the numbers on the five tickets drawn is 24, is

There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7 th drawn ball is 4 th white, is

If $P(B)=\frac{3}{5}, P(A / B)=\frac{1}{2}$ and $P(A \cup B)=\frac{4}{5}$, then $P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)$ is equal to

Two numbers $a$ and $b$ are chosen at random from the set $\{1,2,3, \ldots, 5 n\}$. The probability that $a^4-b^4$ is divisible by 5, is

In tossing 10 coins, the probability of getting exactly 5 heads is

Suppose $A$ and $B$ are two events such that $P(A)>0$ and $P(B) \neq 1$, then $P\left(A^{\prime} \mid B^{\prime}\right)$ equals

Let $x$ be a non-zero real number. A determinant is chosen from the set of all determinants of order 2 with entries $x$ or $-x$ only. The probability that the value of the determinant is non-zero is

A bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag replacing the ball each time after the draw till one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$, then the ratio $a:b$ is

Which one is not a requirement of a binomial distribution?

If $P(A)=0.4$, and $P(A \cap B)=0.15$, then $P\left(A \mid A^{\prime} \cup B^{\prime}\right)$ is equal to

Let $E_1, E_2$ and $E_3$ be any pairwise independent events with $P\left(E_1\right)>0$ and $P\left(E_1 \cap E_2 \cap E_3\right)=0$, then $P\left(\bar{E}_2 \cap \bar{E}_3 / E_1\right)$ is equal to

Two cards are drawn without replacement from a well-shuffled pack. The probability that one of them is an ace of heart, is

The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively. If $P(X=1)=\frac{4}{243}$, then $P(X=4$ or 5$)$ is equal to :

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in $2 \times 2$ matrices. The probability that such formed matrices have all different entries and are non-singular, is

A die is thrown.

I. The probability of a prime number will appear is $\frac{1}{2}$.

II. The probability of a number more than 6 will appear is $1.$

In an experiment the success is twice that of failure. If the experiment is repeated 6 times, the probability that at least 4 times favourable is

If the probability distribution of a random variable $\mathrm{X}$ is as given below:
$\begin{array}{cccccccccccccccccccc} {X = x:}&{ - 2}&{ - 1}&0&1&2&3 \\ {P(X = x):}&{\frac{1}{{10}}}&k&{\frac{1}{5}}&{2k}&{\frac{3}{{10}}}&k \end{array}$
Then the value of $k$, is

One mapping is selected at random from all mappings of the set $S=\{1,2, \ldots ., n\}$ to itself. If the probability that the mapping is one-one is $\frac{5}{324}$ then the value of $n$ equals $(n \in N)$

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn, is

A and B throw a dice. The probability that A's throw is not greater than B's, is

The probability that a year chosen at random has 53 Sundays, is

If $P(A)=\frac{3}{10}, P(B)=\frac{2}{5}$ and $P(A \cup B)=\frac{3}{5}$, then $P(B / A)+P(A / B)$ equals to

In a survery, it was found that 21 persons liked product $A$, 26 liked product $B$ and 29 liked product $C$. If 14 persons liked products $A$ and $B,$ 12 liked products $C$ and $A,$ 13 persons liked products $B$ and $C$ and 8 liked all the three products then
(i) Find the number of persons who liked the product $C$ only
(ii) The number of persons who like the products ${A}$ and ${B}$ but not ${C}$

In a poisson distribution mean is 16, then standard deviation is

A three digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same, is

Bag $\mathrm{P}$ contains 6 red and 4 blue balls and bag $\mathrm{Q}$ contains 5 red and 6 blue balls. A ball is transferred from bag P to bag $\mathrm{Q}$ and then a ball is drawn from bag $Q$. What is the probability that the ball drawn is blue?

A number is selected at random from the first twenty-five natural numbers. If it is a composite number, then it is divided by 5 . But if it is not a composite number, then it is divided by 2 . The probability that there will be no remainder in the division, is

It is given that the events $A$ and $B$ are such that $P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}$ and $P(B / A)=\frac{2}{3}$. Then, $P(B)$ is

If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^2+\alpha x+\beta>0$, for all $x \in R$, is :

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $\frac{k}{3^{11}}$, then $k$ is equal to