Probability & Statistics PYQ — Page 13

If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is :

If the data ${x}_{1},{x}_{2},\ldots {x}_{10}$ is such that the mean of first four of these is $11,$ the mean of the remaining six is $16$ and the sum of squares of all of these is $2000$, then the standard deviation of this data is:

A student scores the following marks in five tests: $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is $48$ in the six tests, then the standard deviation of the marks in six tests is:

An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

If both the mean and the standard deviation of $50$ observations ${x}_{1}, {x}_{2}, \ldots , {x}_{50}$ are equal to $16$, then the mean of ${({x}_{1}-4)}^{2}, {({x}_{2}-4)}^{2}, \ldots ,{({x}_{50}-4)}^{2}$ is

The mean and variance for seven observations are $8$ and $16$ respectively. If $5$ of the observations are $2,4,10,12,14,$ then the product of the remaining two observations is

$5$ students of a class have an average height $150 cm$ and variance $18 c{m}^{2}.$ A new student, whose height is $156 cm,$ joined them. The variance $(in c{m}^{2})$ of the height of these six students is:

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1,2,3,\ldots ,9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3,4$ and $4$; then the absolute value of the difference of the other two observations, is :

Two integers are selected at random from the set $\{1,2, \ldots, 11\}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

The mean of a set of $30$ observation is $75$. If each observations is multiplied by non-zero number $\lambda$ and then each of them is decreased by $25$, their mean remains the same. Then, $\lambda$ is equal to :

If the mean of the data: $7,8,9,7,8,7, \lambda, 8$ is 8 , then the variance of this data is

If $\sum _{i=1}^{9}({x}_{i}-5)=9$ and $\sum _{i=1}^{9}{({x}_{i}-5)}^{2}=45$, then the standard deviation of the $9$ items ${x}_{1}, {x}_{2},\ldots .,{x}_{9}$ is

A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $B$ is :

Two different families $A$ and $B$ are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family $B$ is $\frac{1}{12},$ then the number of children in each family is

A box ' $A$ ' contanis 2 white, 3 red and 2 black balls. Another box ' $B^{\prime}$ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box ' $B^{\prime}$ is

The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number $\lambda$ and then each of them is decreased by 25 , their mean remains the same. The $\lambda$ is equal to equal to $\{0\}$

A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If $X$ starts the game, and the probability of winning the game by both the players is equal, then the value of ' $p$ ' is

The mean and the standard deviation $(S.D.)$ of five observations are $9$ and $0$, respectively. If one of the observation is increased such that the mean of the new set of five observations becomes $10$, then their $S.D.$ is

Let $A, B$ and $C$ be three events, which are pair-wise independent and $\bar{E}$ denotes the complement of an event $E$. If $P(A\cap B\cap C)=0$ and $P(C)>0,$ then $P[(\bar{A}\cap \bar{B})|C]$ is equal to

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:

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: