JEE Main Mathematics — Probability & Statistics previous year questions with solutions.
From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is :
If two different numbers are taken from the set ${0,1,2,3,.....,10}$; then the probability that their sum as well as absolute difference are both multiple of $4$, is:
Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by P or Q but not by R is:
For three events, $A, B$ and $C,$ $P$(Exactly one of $A$ or $B$ occurs) $=P$(Exactly one of $B$ or $C$ occurs) $=P$(Exactly one of $C$ or $A$ occurs) $=\frac{1}{4}$ and $P$(All the three events occur simultaneously) $=\frac{1}{16}.$ Then the probability that at least one of the events occurs, is:
The sum of $100$ observations and the sum of their squares are $400&2475$, respectively. Later on, three observations $3,4&5$ were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations 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:
If $A$ and $B$ are any two events such that $P(A)=\frac{2}{5}$ and $P(A\cap B)=\frac{3}{20},$ then the conditional probability, $P(A|({A}^{'}\cup {B}^{'})),$ where ${A}^{'}$ denotes the complement of $A$, is equal to :
The mean of $5$ observations is $5$ and their variance is $12.4$. If three of the observations are $1,2&6$; then the value of the remaining two is :
Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If ${E}_{1}$ is the event that die $A$ shows up four, ${E}_{2}$ is the event that die $B$ shows up two and ${E}_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?
If the standard deviation of the numbers $2,3,a$ and $11$ is $3.5$, then which of the following is true ?
If the mean deviation of the numbers $1, 1+d,\ldots , 1+100d$ from their mean is $255$, then a value of $d$ is :
If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is
Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X)$, with replacement, then the probability that $A$ and $B$ have equal number of elements is:
If the mean and the variance of a binomial variate $X$ are $2&1$ respectively, then the probability that $X$ takes a value greater than or equal to one is:
If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is:
A factory is operating in two shifts, day and night, with $70$ and $30$ workers, respectively.If per day mean wage of the day shift workers is, $₹54$ and per day mean wage of all the workers is $₹60$, then per day mean wage of the night shift workers (in $₹$) is :
The mean of a data set comprising of $16$ observations is $16$. If one of the observation value $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data is
Let $A$ and $E$ be any two events with positive probabilities Statement I: $P(E/A)\geq P(A/E)P(E).$ Statement II: $P(A/E)\geq P(A\cap E).$
A set $\mathrm{S}$ contains 7 elements. A non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $\mathrm{x} \in \mathrm{A}$ is:
The variance of the first $50$ even natural numbers is :
If $A$and $B$ are two events such that $P(A\cup B)=P(A\cap B)$, then the incorrect statement amongst the following statements is :
Let $\bar{X}$ and M.D. be the mean and the mean deviation about $\bar{X}$ of $n$ observations $\mathrm{x}_{\mathrm{i}}, \mathrm{i}=1,2$,n. If each of the observations is increased by 5 , then the new mean and the mean deviation about the new mean, respectively, are :
If $X$ has a binomial distribution, $B(n, p)$ with parameters $n$ and $p$ such that $P(X=2)=P(X=3)$, then $\mathrm{E}(\mathrm{X})$, the mean of variable $\mathrm{X}$, is
A number $\mathrm{x}$ is chosen at random from the set $\{1$, $2,3,4, \ldots ., 100\}$. Define the event: $\mathrm{A}=$ the chosen number $x$ satisfies $\frac{(x-10)(x-50)}{(x-30)} \geq 0$ Then $\mathrm{P}(\mathrm{A})$ is: