Probability & Statistics PYQ — Page 13

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:

If the mean and standard deviation of $5$ observations ${x}_{1},{x}_{2}, {x}_{3}, {x}_{4}, {x}_{5}$ are $10$ and $3,$ respectively, then the variance of $6$ observations ${x}_{1}, {x}_{2}, \ldots , {x}_{5}$ and $-50$ is equal to

Two cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals:

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

If the probability of hitting a target by a shooter, in any shot is $\frac{1}{3},$ then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than $\frac{5}{6},$ 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:

Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls 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

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

Let $\mathrm{S}=\{1,2, \ldots . ., 20\}$. A subset $\mathrm{B}$ of $\mathrm{S}$ is said to be "nice", if the sum of the elements of $\mathrm{B}$ is 203 . Than the probability that a randomly chosen subset of $S$ is "nice" is :

If the standard deviation of the numbers $-1,0,1,k$ is $\sqrt{5}$ where $k>0,$ then $k$ is equal to

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 :

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

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

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 :

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 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

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

If the mean of the data: $7,8,9,7,8,7, \lambda, 8$ is 8 , then the variance of this data 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 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 age of $25$ teachers in a school is $40$ years. A teacher retires at the age of $60$ years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is $39$ years, then the age (in years) of the newly appointed teacher is

Let $E&F$ be two independent events. The probability that $E&F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2}$ , then a value of $\frac{P(E)}{P(F)}$ is: