JEE Main Mathematics — Probability & Statistics previous year questions with solutions.
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is
Four numbers are chosen at random (without replacement) from the set $\{1,2,3, \ldots ., 20\}$. Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$. Statement-2: If the four chosen numbers from an AP, then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5\}$.
If the mean deviation of number $1,1+d, 1+2 d, \ldots ., 1+100 d$ from their mean is 255 , then the $d$ is equal to
Statement-1 : The variance of first $n$ even natural numbers is $\frac{n^2-1}{4}$ Statement-2 : The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2 n+1)}{6}$
One ticket is selected at random from 50 tickets numbered $00,01,02, \ldots, 49$. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals
A die is thrown. Let $A$ be the event that the number obtained is greater than 3 . Let $B$ be the event that the number obtained is less than 5 . Then $P(A \cup B)$ is
The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.80$. Then which one of the following gives possible values of $a$ and $b$ ?
It is given that the events $A$ and $B$ are such that $P(A)=\frac{1}{4}, P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{2}{3}$. Then $P(B)$ is
A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is
The average marks of boys in a class is $52$ and that of girls is $42$. The average marks of boys and girls combined is $50$. The percentage of boys in the class is
At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is
Suppose a population $A$ has 100 observations $101,102, \ldots, 200$, and another population $B$ has 100 observations $151,152, \ldots, 250$. If $V_A$ and $V_B$ represent the variances of the two populations, respectively, then $\frac{V_A}{V_B}$ is
A random variable $X$ has Poisson distribution with mean 2. Then $P(X>1.5)$ equals
If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
Let $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ be $\mathrm{n}$ observations such that $\sum \mathrm{x}_{\mathrm{i}}^2=400$ and $\sum \mathrm{x}_{\mathrm{i}}=80$. Then a possible value of $\mathrm{n}$ among the following is
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
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
In a series of $2 n$ observations, half of them equal a and remaining half equal $-a$. If the standard deviation of the observations is 2 , then $|a|$ equals
A random variable $X$ has the probability distribution: \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}: & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \mathrm{p}(\mathrm{X}): & 0.15 & 0.23 & 0.12 & 0.10 & 0.20 & 0.08 & 0.07 & 0.05 \\ \hline \end{array} For the events $E=\{X$ is a prime number $\}$ and $F=\{X < 4\}$, the probability $P(E \cup F)$ is
Consider the following statements: Mode can be computed from histogram Median is not independent of change of scale Variance is independent of change of origin and scale.
The probability that A speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is
In an experiment with 15 observations on $x$, the following results were available: $\Sigma x^2=2830, \Sigma x=170$ One observation that was 20 was found to be wrong and was replaced by the correct value 30 . The corrected variance is
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
The median of a set of 9 distinct observations is $20.5$. If each of the largest 4 observations of the set is increased by 2 , then median of the new set