Probability practice · Medium

Four boys and three girls stand in a queue for an interview, probability that they will in alternate position, is

A missile is destroyed before hitting the target by a probability of $\frac{1}{3}$. If the missile is not destroyed probability of hitting the target is $\frac{3}{4}$. Three missiles are fired. The probability of exactly two hits the target is

$A$ is a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are chosen at random. ($P$ and $Q$ may have elements in common). The probability that $P \cap Q=$ $\phi$ is

The probability that two randomly selected subsets of the set $\left\{ {1,2,3,4,5} \right\}$ have exactly two elements in their intersection, is

The mean and variance of 5 observations of an experiment are 4 and 5.2 respectively. If from these observations three are 1,2 and 6 , then the mean of remaining will be-

Two different families $A$ and $B$ are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket.
If the probability that all the tickets go to the children of the family $B$ is $\frac{1}{12}$, then the number of children in each family is?

The probability of a man hitting a target is $\frac{2}{5}$. He fires at the target $k$ times ( $k$, a given number). Then the minimum $k$, so that the probability of hitting the target at least once is more than $\frac{7}{10}$, is :

A dice is rolled 4 times, the numbers appearing are listed. The number of different throws, such that the largest number appearing in the list is 4 , is

Twelve tickets are numbered from 1 to 12. One ticket is drawn at random, then the probability of the number to be divisible by 2 or 3, is

If 3 numbers are selected from the set $(1,2,3,........., 24)$ without replacement, then what is the probability that the selected numbers do not form an A.P.?

If $\mathrm{P}(\mathrm{A})=\frac{2}{5}, \mathrm{P}(\mathrm{B})=\frac{3}{10}$ and $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{5}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}^{\prime}\right) \cdot \mathrm{P}\left(\mathrm{B}^{\prime} \mid \mathrm{A}^{\prime}\right)$ is equal to

There are $m$ persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are not together is

There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at radndom. The probability that there is at least one pair is

A letter is taken at random from the letters of the word 'STATISTICS' and another letter is taken at random from the letters of the word 'ASSISTANT'. The probability that they are the same letter is

For the married couple living in Jammu, the probability that a husband will vote in an election is 0.5 and the probability that his wife will vote is 0.4 . The probability that the husband votes, given that his wife also votes is 0.7 . Then the probability that husband and wife both will vote is

Three are six verities of a regular hexagon are chosen at random, then the possibility that the triangle with three vertices is equilateral, is equal to

A person draws a card from a pack, replaces it, shuffles the pack, again draws a card, replaces it and draws again. This he does until he draws a heart. The probability that he will have to make at least four draws is

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is

A letter is taken out at random from ‘ASSISTANT’ and another is taken out from ‘STATISTICS’. The probability that they are same letters, is

Six faces of a die are marked with the numbers $1,-1,0,-2,2$ and 3 . The die is thrown thrice. The probability that the sum of the numbers thrown is six, is

A coin is tossed $2n$ times. The chance that the number of times one gets head is not equal to the number of times one gets tail, is

The probability that a man will live 10 more years is 1/4 and the probability that his wife will live 10 more years is 1/3. Then the probability that neither will be alive in 10 years, is

Consider two events $A$ and $B$ such that $P\left( A \right) = \frac{1}{4},\;P\left( {\frac{B}{A}} \right) = \frac{1}{2},\;P\left( {\frac{A}{B}} \right) = \frac{1}{4}.$ For each of the following statements, which is true?
1. $P\left( {{A^c} + {B^c}} \right) = \frac{3}{4}\;$
2. The events $A$ and $B$ are mutually exclusive.
3. $P(A/B)\, + \,P(A/{B^c})\, = \,1$

If $A$ and $B$ are two events such that $P\left( A \right) \ne 0$ and $P\left( B \right) \ne 1,$ then $P\overline {\left( {\frac{A}{B}} \right)}$ is equal to

The coefficients $a, b, c$ in the quadratic equation $a x^2+b x+c=0$ are chosen from the set
$\{1,2,3,4,5,6,7,8\}.$ The probability of this equation having repeated roots is:

Two dice are thrown simultaneously. What is the probability of obtaining a multiple of 2 on one of them and a multiple of 3 on the other

Let ${p}$ denote the probability that a man aged $x$ years will die in a year. The probability that out of ${n}$ men ${A}_1,{A}_2, {A}_3, \ldots \ldots {A}_n$ each aged $x, {A}_1$ will die in a year and will be the first to die is

A bag contains 10 white and 3 black balls. Balls are drawn one-by-one without replacement till all the black balls are drawn. The probability that the procedure of drawing balls will come to an end at the seventh draw is

A bag contains 5 white, 3 black balls. 2 balls are drawn one by one, their colour noted and
replaced in bag then probability that one ball is white and one is black, is

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