List of top Statistical Science Questions on Probability asked in ICAR AIEEA (PG)

If \(A\) and \(B\) are two events such that \[ P(A \cup B)=\frac{5}{6}, \qquad P(A \cap B)=\frac{1}{3}, \qquad P(B')=\frac{1}{2}, \] then the events \(A\) and \(B\) are:

If \(X\) is a random variable with probability density function \[ f(x)=\frac{1}{\sqrt{12\pi}}\,e^{-\frac{(x-1)^2}{12}}, \qquad 0<x<\infty, \] then the value of \[ \int_{1}^{\infty} f(x)\,dx \] is:

The annual precipitation data of a city is normally distributed with mean 1200 mm and standard deviation 200 mm. The probability that annual precipitation will be more than 1400 mm is

If \(X\) is a normal random variable with mean 50 and variance 25, then \(P(X \le 55)\) is

A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes is

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is:

A random variable \(X\) has the following pdf:
\[ f(x) = \frac{1}{\sqrt{12\pi}} e^{-\frac{(x-1)^2}{6}}; \quad -\infty < x < \infty \]
\(= 0\), otherwise.
Then \(\int_{1}^{\infty} f(x)dx = ?\)

The annual precipitation data of a city is normally distributed with mean \(1200\text{mm}\) and standard deviation \(200\text{mm}\), respectively. The probability that annual precipitation will be more than \(1400\text{mm}\)

A bowl contains eight chips. Three of the chips are red and the remaining five are blue. Two chips are to be drawn successively, at random and without replacement. What is the probability that the first draw results in a red chip and that the second draw results in a blue chip?

The probability of occurrence of two events \(A\) and \(B\) are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither \(A\) occurs nor \(B\) occurs is:

A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes is:

If \(X\) is a random Poisson variate with \(P(X=1) = P(X=2)\). Then \(P(X=4)\) is:

Two dice are rolled simultaneously. What is the probability that the sum of numbers on dice is 9?

Given \(P(A) = p_1, P(B) = p_2\) and \(P(AB) = p_3\). Then \(P(A' \cap B')\) will be:

If $C_1$ and $C_2$ are subset of sample space S. Then which is correct:

Two unbiased dice are thrown simultaneously. Then the possible number of outcomes will be:

A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the probability of wife's selection is (1/5). What is the probability that only one of them is selected ?

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : The probability of a sure event is 1.
Reason (R) : Let E be an event. Then \(0 \le P(E) \le 1\).
In light of the above statements, choose the correct answer from the options given below:

A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all the questions randomly by guessing the answer to each question. Which of the following probability distributions can be used to calculate the student’s chance of getting at least 20 questions right ?

The probability of selecting an item in probability sampling, from the population is :

In a Poisson Distribution, if mean = e, then P(x) is given by ____________.

When Viswanath plays chess, he wins with probability 0.80, loses with probability 0.20. Assume independence, find the probability that Viswanath's first win happens when he plays his third game.

Which of the following is not a characteristic of the normal distribution ?

In a normal distribution 10.03% of the items are under 35kg weight and 89.97% of the items are under 80kg weight. What are the mean and standard deviation of the distribution ?

Let the moment generating function (m.g.f) of a random variable is of the form \(M_X(t)=(0.4e^t +0.6)^8\). Find the mean and variance of a random variable Y=3X+2.