List of top Mathematics Questions on Probability asked in MHT CET

The differential equation of all straight lines passing through the point \( (1, -1) \) is

If $f(x) = \begin{cases} \frac{1-\cos 4x}{x^2} & , \text{if } x<0 \\ a & , \text{if } x = 0 \\ \frac{(16+\sqrt{x})^{\frac{1}{2}}-4}{\sqrt{x}} & , \text{if } x>0 \end{cases}$ is continuous at $x = 0$, then a =}

If p : switch $S_1$ is closed, q : switch $S_2$ is closed, r : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to

The equations of the tangents to the circle $x^2 + y^2 = 36$ which are perpendicular to the line $5x + y = 2$, are

If matrix $A = \frac{1}{11} \begin{bmatrix} -1 & 7 & -24 \\ 2 & a & 4 \\ 2 & -3 & 15 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 3 & 3 & 4 \\ 2 & -3 & 4 \\ b & -1 & c \end{bmatrix}$, then the values of $a, b, c$ respectively are ..............

Three numbers are chosen at random from numbers 1 to 20. The probability that they are consecutive is

A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?

Choose a randomly selected leap year, in which 52 Saturdays and 53 Sundays are to be there. Given the following probability distribution:

Find the mean and standard deviation.

If a random variable X has the following probability distribution values:

X	0	1	2	3	4	5	6	7
P(X)	1/12	1/12	1/12	1/12	1/12	1/12	1/12	1/12

Then P(X ≥ 6) has the value:

A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?

If \( P(A \cap B) = \frac{2}{25} \) and \( P(A \cup B) = \frac{8}{25} \), then find the value of \( P(A) \).

A boy tries to message his friend. Each time, the chance the message is delivered is \( \frac{1}{6} \), and the chance it fails is \( \frac{5}{6} \). He sends 6 messages. Find the probability that exactly 5 messages are delivered.

In a dataset of 50 values, the mean is 40 and the variance is 25. What is the probability that a randomly selected value from this dataset is between 35 and 45?

In the word "UNIVERSITY", find the probability that the two "I"s do not come together.

A die is rolled once. What is the probability of rolling a number greater than 4?

A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?

A die is rolled. What is the probability of getting a number less than or equal to 4?

If two dice are rolled, what is the probability of getting a sum of 7?

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:

The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:

The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

Let \( F(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix} \), where \( \alpha \in \mathbb{R} \). Then \( [F(\alpha)]^{-1} \) is equal to:

If the mean and variance of a Binomial variate \(X\) are 2 and 1 respectively, then the probability that \(X\) takes a value greater than 1 is:

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is:

Find the expected value and variance of \( X \) for the following p.m.f: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline P(X) & 0.2 & 0.3 & 0.1 & 0.15 & 0.25 \\ \hline \end{array} \]