Mathematics Probability & Statistics questions from JEE Main 2013.
Mean of 5 observations is 7 . If four of these observations are $6,7,8,10$ and one is missing then the variance of all the five observations is :
$\mathrm{A}, \mathrm{B}, \mathrm{C}$ try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are $\frac{3}{4}, \frac{1}{2}, \frac{5}{8}$. The probability that the target is hit by A or B but not by $\mathrm{C}$ is :
The mean of a data set consisting of 20 observations is 40 . If one observation 53 was wrongly recorded as 33 , then the correct mean will be:
If the median and the range of four numbers $\{x, y, 2 x+y, x-y\}$, where $0 < y < x < 2 y$, are 10 and 28 respectively, then the mean of the numbers 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 :
In a set of $2 n$ observations, half of them are equal to ' $\mathrm{a}$ ' and the remaining hall are equal to ' $-\mathrm{a}^{\prime}$ '. If the standard deviation of all the observations is 2 ; then the value of $|a|$ is :
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?
If the events $\mathrm{A}$ and $\mathrm{B}$ are mutually exclusive events such that $\mathrm{P}(\mathrm{A})=\frac{3 x+1}{3}$ and $\mathrm{P}(\mathrm{B})=\frac{1-x}{4}$, then the set of possible values of $x$ lies in the interval :
Given two independent events, if the probability that exactly one of them occurs is $\frac{26}{49}$ and the probability that none of them occurs is $\frac{15}{49}$, then the probability of more probable of the two events is :