Probability practice · Mixed difficulty

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 $(n \in N)$

India plays two matches each with the West Indies and Australia. In any match, the probabilities of India getting 0,1 and 2 points are 0.45,0.05 and 0.50, respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points, is

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

Two small squares on a chess board are chosen at random. Then, the probability that they have a common side, 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

If the numbers $1,2,3,4,5,6$ are arranged in a circle, then the probability that the sum of any two consecutive numbers must not be equal to 7 is

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 ${C}$

Two distinct numbers are chosen at random from the first 15 natural numbers. The probability that the sum will be divisible by 3 is

A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box without replacement. The probability that they are alternatively either {odd, even, odd} of {even, odd, even} is

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

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, 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?

Let $A, B$ and $C$ be three events such that $P(C)=0$.

Statement-1: $P(A \cap B \cap C)=0$

Statement-2: $P(A \cup B \cup C)=P(A \cup B)$

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

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 events $A$ and $B$ are

Two numbers are randomly selected from
the first 100 natural numbers. The probability that the
product of the numbers is divisible by 7 is