Probability & Statistics PYQ — Page 5

There are three bags $X, Y$ and $Z$. Bag $X$ contains 5 one-rupee coins and 4 five-rupee coins; Bag $Y$ contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag Y, is :

The frequency distribution of the age of students in a class of 40 students is given below. $\begin{array}{|l|c|c|c|c|l|l|} \hline \text{Age} & 15 & 16 & 17 & 18 & 19 & 20 \\ \hline \text{No of Students} & 5 & 8 & 5 & 12 & x & y \\ \hline \end{array}$ If the mean deviation about the median is 1.25, then $4 x+5 y$ is equal to :

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed $3$ times, then the probability of getting two tails and one head is-

Let Ajay will not appear in JEE exam with probability $p=\frac{2}{7},$ while both Ajay and Vijay will appear in the exam with probability $q=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is:

Let $M$ denote the median of the following frequency distribution. $\begin{matrix}\text{ Class } & 0-4 & 4-8 & 8-12 & 12-16 & 16-20 \\ \text{ Frequency } & 3 & 9 & 10 & 8 & 6\end{matrix}$ Then $20M$ is equal to :

A company has two plants $A$ and $B$ to manufacture motorcycles. $60 \%$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $B .80 \%$ of the motorcycles manufactured at plant $A$ are rated of the standard quality, while $90 \%$ of the motorcycles manufactured at plant $B$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $p$ is the probability that it was manufactured at plant $B$, then $126 p$ is

Bag$A$ contains $3$ white, $7$ red balls and bag $B$ contains $3$ white, $2$ red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag $A$, if the ball drawn in white, is :

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn $\mathrm{A}$ is :

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is:

Let $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked $1,2,3,4$. If the probability that $a x^2+b x+c=0$ has all real roots is $\frac{m}{n}$, $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to ________

A fair die is thrown until $2$ appears. Then the probability, that $2$ appears in even number of throws, is

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 :

If the variance of the frequency distribution $\begin{array}{|c|c|c|c|c|c|c|} \hline x & c & 2 c & 3 c & 4 c & 5 c & 6 c \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$ is 160, then the value of $c \in N$ is

Two dice $A$ and $B$ are rolled. Let the numbers obtained on $A$ and $B$ be $\alpha$ and $\beta$ respectively. If the variance of $\alpha -\beta$ is $\frac{p}{q},$ where $p$ and $q$ are co-prime, then the sum of the positive divisors of $p$ is equal to

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2,\sqrt{3N},N+2$ are in geometric progression be $\frac{k}{48}$. Then the value of $k$ is

The variance of the data 2, 4, 6, 8, 10 is:

The standard deviation of 5 observations 1, 2, 3, 4, 5 is:

Let $S={{w}_{1},{w}_{2},\ldots .}$ be the sample space associated to a random experiment. Let $P({w}_{n})=\frac{P({w}_{n-1})}{2},n\geq 2$. Let $A={2k+3l;k,l\in \mathbb{N}}$ and $B={{w}_{n};n\in A}$. Then $P(B)$ is equal to

A fair $n(n>1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$, then $n$ is equal to

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q},$ where $p$ and $q$ are co-prime, then $q-p$ is equal to

Let $S$ be the set of all values of ${a}_{1}$ for which the mean deviation about the mean of $100$ consecutive positive integers ${a}_{1},{a}_{2},{a}_{3},\ldots .,{a}_{100}$ is $25$ . Then $S$ is

Let $9={x}_{1}<{x}_{2}<\ldots <{x}_{7}$ be in an A.P. with common difference $d$. If the standard deviation of ${x}_{1},{x}_{2}\ldots ,{x}_{7}$ is 4 and the mean is $\bar{x}$, then $\bar{x}+{x}_{6}$ is equal to :

The mean and standard deviation of $10$ observations are $20$ and $8$ respectively. Later on, it was observed that one observation was recorded as $50$ instead of $40$. Then the correct variance is

If the variance of the frequency distribution <table class="pyq-table"><tbody><tr><td>${x}_{i}$</td><td>$2$</td><td>$3$</td><td>$4$</td><td>$5$</td><td>$6$</td><td>$7$</td><td>$8$</td></tr><tr><td>Frequency ${f}_{i}$</td><td>$3$</td><td>$6$</td><td>$16$</td><td>$\alpha$</td><td>$9$</td><td>$5$</td><td>$6$</td></tr></tbody></table>is $3$, then $\alpha$ is equal to