JEE Main Mathematics — Probability & Statistics previous year questions with solutions.
The mean and variance of $8$ observations are $10$ and $13.5,$ respectively. If $6$ of these observations are $5,7,10,12,14,15,$ then the absolute difference of the remaining two observations is :
In a box, there are $20$ cards, out of which $10$ are labelled as $A$ and the remaining $10$ are labelled as $B$ . Cards are drawn at random, one after the other and with replacement, till a second $A$ card is obtained. The probability that the second $A$ card appears before the third $B$ card is:
In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$ . If the probability that at most two machines will be out of service on the same day is ${(\frac{3}{4})}^{3}k,$ then $k$ is equal to
For the frequency distribution: Variate $(x):{x}_{1},{x}_{2},{x}_{3},\ldots ,{x}_{15}$ Frequency $(f):{f}_{1},{f}_{2},{f}_{3},\ldots ,{f}_{15}$ where $0<{x}_{1}<{x}_{2}<{x}_{3}<\ldots <{x}_{15}=10$ and $\sum _{i=1}^{15}{f}_{i}>0,$ the standard deviation cannot be
Box $1$ contains $30$ cards numbered $1$ to $30$ and Box $2$ contains $20$ cards numbered $31$ to $50$. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box $1$ is
Let $X={x\in N:1\leq x\leq 17}$ and $Y={ax+b:x\in X\mathrm{and}a,b\in R,a>0}$. If mean and variance of elements of $Y$ are $17$ and $216$ respectively then $a+b$ is equal to
If $\Sigma _{i=1}^{n}({x}_{i}-a)=n$ and $\Sigma _{i=1}^{n}{({x}_{i}-a)}^{2}=na,(n,a>1)$, then the standard deviation of $n$ observations ${x}_{1},{x}_{2},\ldots ,{x}_{n}$ is
Consider the data on $x$ taking the values $0,2,4,8,.....,{2}^{n}$ with frequencies $C0n,C1n,C2n,....,Cnn$ respectively. If the mean of this data is $\frac{728}{{2}^{n}}$, then $n$ is equal to ....... .
If the mean and the standard deviation of the data $3,5,7,a,b$ are $5$and $2$ respectively, then $a$ and $b$ are the roots of the equation:
Let $A$ and $B$, be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$, and the probability that $A$ or $B$, occurs is $\frac{1}{2}$, then the probability of both of them occur together is.
A die is thrown 6 times. The probability of getting at least one six is:
Let ${E}^{C}$ denote the complement of an event $E$. Let ${E}_{1},{E}_{2}$ and ${E}_{3}$ be any pairwise independent events with $P({E}_{1})>0$ and $P({E}_{1}\cap {E}_{2}\cap {E}_{3})=0$ then $P(({E}_{2}^{C}\cap {E}_{3}^{C})/{E}_{1})$ is equal to
If the variance of the following frequency distribution: Class: $10-2020-3030-40$ Frequency: $2x2$ is $50,$ then $x$ is equal to _______
Let ${x}_{i}(1\leq i\leq 10)$ be ten observation of a random variable $X$. If $\sum _{i=1}^{10}({x}_{i}-p)=3$ and $\sum _{i=1}^{10}{({x}_{i}-p)}^{2}=9$ where $0\neq p\in R$, then the standard deviation of these observations is:
The mean and variance of $7$ observations are $8$ and $16$, respectively. If five observations are $2,4,10,12,14$ then the absolute difference of the remaining two observations is :
If the variance of the first $n$ natural numbers is $10$ and the variance of the first $m$ even natural numbers is $16,$ then the value of $m+n$ is equal to
A random variable $X$ has the following probability distribution: $\begin{matrix}\begin{matrix}X: & 1 & \begin{matrix}2 & 3 & \begin{matrix}4 & 5\end{matrix}\end{matrix}\end{matrix} \\ P(X):\begin{matrix}{k}^{2} & \begin{matrix}2k & k & \begin{matrix}2k & 5{k}^{2}\end{matrix}\end{matrix}\end{matrix}\end{matrix}$ Then, $P(X>2)$ is equal to:
If $10$ different balls are to be placed in $4$ distinct boxes at random, then the probability that two of these boxes contain exactly $2$ and $3$ balls is:
Out of 11 consecutive natural number if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference is :
A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of $4$. Then the conditional probability that the score $4$ has appeared at least once is
The probability of a man hitting a target is $\frac{1}{10}.$ The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4},$ is....
Let the observation ${x}_{i}(1\leq i\leq 10)$ satisfy the equations $\sum _{i=1}^{10}({x}_{i}-5)=10$, $\sum _{i=1}^{10}{({x}_{i}-5)}^{2}=40$ . If $\mu$ and $\lambda$ are the mean and the variance of the observations, ${x}_{1}-3,{x}_{2}-3,....,{x}_{10}-3,$ then the ordered pair $(\mu ,\lambda )$ is equal to:
If the mean and variance of eight numbers $3,7,9,12,13,20,x$ and $y$ be $10$ and $25$ respectively, then $x\cdot y$ is equal to
If the variance of the terms in an increasing $A.P.$ ${b}_{1}{b}_{2},{b}_{3},\ldots \ldots ..,{b}_{11}$ is $90$ then the common difference of this $A.P.$ is