Question 1 :
Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total of 12 is
Question 2 :
For two data sets, each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
Question 3 :
There is an objective type question with 4 answer choices exactly one of which is correct. A student has not studied the topic on which the question has been set. The probability that the student guesses the correct answer, is
Question 4 :
If A and B are two independent events, then the probability that only one of A and B occur is
Question 5 :
Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest number appearing on a selected coupon be 9, is
Question 6 :
If the variance of 1, 2, 3, 4, 5, ..., 10 is $\frac{99}{12}$, then the standard derivation of 3, 6, 9, 12, ..., 30 is
Question 7 :
The probability that number selected at random from the numbers 1, 2, 3, 4, 5, 6, 7, 8, ……., 100 is a prime, is
Question 8 :
From a group of 8 boys and 3 girls, a committee of 5 members to be formed. Find the probability that 2 particular girls are included in the committee
Question 9 : <p>Following are the marks obtained by 9 students in Mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59</p> <p>The mean deviation from the median is</p>
Question 10 :
Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is
Question 11 :
A random variable X follows binomial distribution with mean α and variance β.Then
Question 12 :
If there exists a linear statistical relationship between two variable x and y, then the regression coefficient of yon x is
Question 13 :
A and B are two independent events such that $P\left( A \right)\frac{1}{2}$ and $P\left( B \right) = \frac{1}{3},\ \text{then}\ P$(neither A nor B)is equal to
Question 14 :
If P(A) = 1/3, P(B) = 1/2 and P(A∪B) = 5/6, then events A and B are
Question 15 :
A card is drawn from a pack of cards. The probability that the card will be a queen or a heart, is
Question 16 :
If the mean and standard deviation of a binomial distribution are 12 and 2 respectively, then value of its parameter p is
Question 17 :
If three natural numbers from 1 to 100 are selected randomly, then probability that all are divisible by both 2 and 3, is
Question 18 :
The standard deviation of n observations x<sub>1</sub>, x<sub>2</sub>, ….., x<sub>n</sub> is 2. If $\text{\ \ }\sum_{i = 1}^{n}{x_{i} = 20}$ and $\sum_{i = 1}^{n}{x_{i}^{2} = 100}$, then n is
Question 19 :
Consider any set of 201 observationsx<sub>1</sub>, x<sub>2</sub>, …x<sub>200</sub>, x<sub>201</sub>. It is given that x<sub>1</sub> < x<sub>2</sub> < … < x<sub>200</sub> < x<sub>201</sub>. Then, the mean deviation of this set of observations about a point k is minimum when k equals
Question 20 :
A random variate X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X=3) = 2P(X = 1) and P(X=2) = 0.3,then P(X = 0) is equal to
Question 21 :
If the variable takes the values 0, 1, 2, …., n with frequencies proportional to the binomial coefficients C(n,0), C(n,1), C(n,2), ….., C(n, n) respectively, then the variance of the distribution is
Question 22 :
The probabilities that a student will obtain grades A, B, C or D are 0.30, 0.35, 0.20 and 0.15 respectively. The probability that he will receive atleast C grade, is
Question 23 :
Two cards are drawn successively with replacement from a well shuffled deck of 52 cards, then the mean of the number of aces is
Question 24 :
In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is
Question 25 :
If var(x)=8.25, var(y)=33.96 and cov(x,y) = 10.2 then the correlation coefficient is
Question 27 :
There are four machines and it is known that exactly two of them are faulty. They are tested, one by one in a random order till both the faulty machines are identified. Then, the probability that only two tests are needed, is
Question 28 :
If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the mean of last three observations is
Question 29 :
Probability of throwing 16 in one throw with three dice is
Question 30 :
A bag contains 3 black, 3 white and 2 red balls. One by one, three balls are drawn without replacement. The probability that the third ball is red, is equal to
Question 31 :
If $\ \sum_{}^{}x = 15,\ \sum_{}^{}y = 36,\ \sum_{}^{}\text{xy} = 110,\ n = 5$, then cov(x, y) equals
Question 32 :
One hundred identical coins, each with probability p or showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is
Question 33 :
If M and N are any two events. The probability, that exactly one of them occurs, is
Question 34 :
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?
Question 35 :
A and B appeared for an interview for two posts. The probability of A′s selection is 1/3 and that of B′s selection is 2/5. The probability that only one of them is selected, is
Question 36 :
6 boys and 6 girls sit in a row randomly. The probability that all 6 girls sit together, is
Question 37 :
The mean of 30 given numbers, when it is given that the mean of 10 of them is 12 and the mean of the remaining 20 is 9, is equal to
Question 38 :
If A and B are independent events and P(C) = 0, then
Question 39 :
If the letters of the word ‘MISSISSIPPI’ are written down at random in a row, the probability that four S′s come consecutively is
Question 40 :
What is the probability that when one die is thrown, the number appearing on top is even?
Question 41 :
A letter is taken out at random from `ASSISTANT’ and another is taken out from `STATISTICS’. The probability that they are the same letters is
Question 42 :
Let 0 < P(A) < 1, 0 < P(B) < 1 and P(A∩B) = P(A) + P(B) − P(A)P(B), then
Question 43 :
If y = f(x) be a monotonically increasing or decreasing function of x and M is the median of variable x, then the median of y is
Question 44 : <p>A biased die is tossed and the respective probabilities for various faces to turn up are</p> <p>Face : 1 2 3 4 5 6</p> <p>Probability : 0.1 0.24 0.19 0.18 0.15 0.14</p> <p>If an even face has turned up, then the probability that it is face 2 or face 4, is</p>
Question 45 :
A five digit number is formed by writing the digits 1, 2, 3, 4, 5, in a random order without repetitions. Then the probability that the number is divisible by 4, is
Question 46 :
The quartile deviation of daily wages of 7 persons which are Rs. 12, 7, 15, 10, 17, 17, 25 is
Question 47 : <p>If X and Y are independent binomial variates $B\left( 5,\frac{1}{2} \right)$ and $B\left( 7,\frac{1}{2} \right),$ then</p> <p>P(X + Y = 3) is</p>
Question 48 :
In a book of 500 pages, it is found that there are 250 typing errors. Assume that poisson law holds for the number of errors per page. Then, the probability that a random sample of 2 pages will contain no error, is
Question 49 :
<br/>$\text{If\ }P\left( B \right) = \frac{3}{4},\ P\left( A \cap B \cap \overline{C} \right) = \frac{1}{3}\ \text{and\ }P\left( \overline{A} \cap B \cap \overline{C} \right) = \frac{1}{3},\ \text{then\ }P\left( B \cap C \right)\text{\ is}$<br/>
Question 50 :
If X is a poisson variate with P(X=0) = 0.8, then the variance of X is
