List of practice Questions

A bag contains 6 red, 4 blue and 10 white balls. A ball is picked from the bag at random What is the probability that it is neither white nor blue?

A die is thrown n times. A random variable X denotes the number of times, the number on the dice is greater than 4 and P(X = 1) = 2P(X = 2). The value of n is :

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability of getting a ‘two’ of hearts or a ‘three’ of diamonds ?

Choose odd one out from the following:

Study the following sequence and then answer the question given below:
9 H 7 Z A 9 2 B C H 3 1 X W V 5 T 4 M 6 0 Q 8 F J.
If every fourth letter/number in the above sequence starting from 7 is eliminated, which of the following will be fifth letter/number to the left of the 12th position from your right?

Three dice are thrown. The probability of getting a sum of numbers which is a perfect cube, is:

A pair of dice is thrown 3 times. If getting a doublet is considered a success, then the probability of two successes is :

In a box, consisting 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is :

Two balls are chosen randomly from an urn containing 8 white balls and 4 black balls by a player. Suppose that he wins ₹30 for each black ball selected and loses ₹15 for each white ball selected. The expected value of winning amount is :

Match LIST I with LIST II

List-I		List-II
A	Randomization is used in	I	Unbiased sampling
B	Randomization is not used in.	II	Probability sampling
C	If every element in the population has an equal chance to be part of the selected sample, then the sampling process is called	III	Biased sampling
D	If a sampling process systematically favours certain outcomes over others, then it is called	IV	Non-probability sampling

Choose the correct answer from the options given below

If \(P(A) = \frac{3}{10}\), \(P(B) = \frac{2}{5}\) and \(P(A \bigcup B) = \frac{3}{5}\), then \(P(B|A)+P(A|B)\) is equal to:

Anita and Bikram are two students. Their chances of solving a problem correctly are \(\frac13\) and \(\frac14\) respectively. If their probability of making a common error is  \(\frac{1}{20}\) and they both obtain same answer then the probability that their answer is correct, is :

The mean of the number of heads in a simultaneous toss of three coins is :

If \(P(A)=\frac{3}{10},P(B)=\frac{2}{5}\), and P(A ∪ B) = \(\frac{3}{5}\), then \(P(\frac{B}{A})+P(\frac{A}{B})\) is equal to :

If A and B are events such that \(P(A'UB')=\frac{1}{3}\) and \(P(AUB) = \frac{4}{9}\) then the value of \(P(A') + P(B')\) is:

A coin is tossed 5 times. The probability of getting atleast one head is:

A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B, if A starts first:

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :

The probability of getting a correct answer to a question is \(\frac{x}{12}\). If the probability of not getting the correct answer is \(\frac{2}{3}\), then what is the value of x ?

If P(E)=0.05, what is the probability of 'not E'?

If \(A= \begin{bmatrix}1 & 0 \\[0.3em]-1 & 5 \\[0.3em] \end{bmatrix}\) and \(I= \begin{bmatrix}1& 0\\[0.3em]0& 1\\[0.3em] \end{bmatrix}\) then the value of k so that \(A^2 = 6A + kI\) is given by:

The value of det\((A^2-2A)\),If \(A=\begin{pmatrix}      1 & 3  \\[0.3em]    2  &1  \end{pmatrix}\),is

Let \(A = [a_{ij}]\) be a 2×2 matrix such that \(aij=\frac{|-3i + j|}{2}\)  then \(a_{21}\) is :

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

If, A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I-A)^3+A^2+I\) is: