Probability PYQs - Last 10 Years
MHT CET / Mathematics / Algebra / 274 recent questions
MathematicsAlgebra2017-2026
Practice 274 MHT CET Mathematics questions from Probability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2019-2026
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214 in last 5 years274 in last 10 years
Last 10 Years Probability Questions
Showing 50 of 274 filtered questions.
1Probability
In a certain city, the ratio of men to women is $5:4$. It is found that $80\%$ of men and $90\%$ of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....
MCQ+2 / -02026
2Probability
Let X be a continuous random variable with the probability density function(p.d.f.) given by$f(x) = \begin{cases} kx, & 0 \leq x < 1 \\ k, & 1 \leq x < 2 \\ -kx + 3k, & 2 \leq x < 3 \\ 0, & \text{otherwise} \end{cases}$$P(2 < X \leq 3) = \c...
MCQ+2 / -02026
3Probability
A random variable $X \sim B(n, p)$ follows a binomial distribution with $n = 6$. If $9P(X = 4) = P(X = 2)$, then the probability of success $p$ is..
MCQ+2 / -02026
4Probability
A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 2 or 4 or 6. The probability that player A wins in the long run is
MCQ+2 / -02026
5Probability
For the following probability distribution of a random variable $X$, the Expected value and Variance of $X$ are respectively$X = x\(1\)2\(3\)P(X = x)\(1/5\)2/5$$2/5$
MCQ+2 / -02026
6Probability
Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........
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7Probability
Consider a game of tossing a six sided fair die. If the face that comes up is $6$, the player wins Rs. $36$ and he loses Rs. $k^2$, where $k$ is the face that comes up $k = \{1, 2, 3, 4, 5\}$, then the expected winning amount in this game i...
MCQ+2 / -02026
8Probability
Given the probability density function (p.d.f.) of the random variable X, $f(x) = \dfrac{1}{2a}$, $0 < x < 2a$, $a > 0$$= 0$, otherwise, then which of the following is correct ?
MCQ+2 / -02026
9Probability
If in $6$ trials, X is a binomial random variable which follows the relation $9P(x = 4) = P(x = 2)$, then the probability of failure is...
MCQ+2 / -02026
10Probability
Let $a$ be an integer selected at random from the set $\{0, 1, 2, 3, \ldots, 9\}$. The probability that the equation $ax^2 - ax + 1 = 0$ has real roots is ...
MCQ+2 / -02026
11Probability
Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in bag B. If a ball is now selected at random from bag B then the probability that this ball is white b...
MCQ+2 / -02026
12Probability
Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 & 3. If X denotes the sum of the numbers, then the expected value of X is...
MCQ+2 / -02026
13Probability
The probability that a bomb will hit the target is $0.8$. Out of 6 bombs dropped, probability that at least 1 will miss the target is...
MCQ+2 / -02026
14Probability
If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are $0.6$, $0.5$ and $0.4$ respectively, while the probability of succeeding in both A and B is $0.3$, in both B and C is $0.2$, in both A and C is...
MCQ+2 / -02026
15Probability
Let $F(x)$ be the cumulative distribution function (c.d.f.) of a continuous random variable $X$. If $F(b) = 0.7$ and $P(X > a) = 0.4$, then the value of $P(a < X < b)$ is ...
MCQ+2 / -02026
16Probability
A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...
MCQ+2 / -02026
17Probability
In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to...
MCQ+2 / -02026
18Probability
If the p. d. f. of a continuous random variable X is given by $f(x) = \begin{cases} k(9 + 8x - x^2), & \text{for } -1 \leq x \leq 4 \\ 0, & \text{otherwise} \end{cases}$ then the value of $k$ is $\ldots$
MCQ+2 / -02026
19Probability
A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is $\ldots$
MCQ+2 / -02026
20Probability
A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and $E(X) = 1.2$, then $N = \ldots$
MCQ+2 / -02026
21Probability
If the mean and the variance of a binomial variate X are 1 and 0.75 respectively, then which of the following is true?
MCQ+2 / -02026
22Probability
Three numbers are chosen from 1 to 30. The probability that minimum is 10 and maximum is 26 is _______
MCQ+2 / -02026
23Probability
If a discrete random variable $X$ takes the values $1, 2, 3, 4$ such that $2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4)$, then $P(X = 4) = \ldots$
MCQ+2 / -02026
24Probability
On average, one out of 10 persons is busy. If six persons are selected at random, then the probability that at least 5 of them will be busy is...
MCQ+2 / -02026
25Probability
Two dice are thrown successively 4 times and getting a doublet is called a success. The probability of getting at least 1 success is
MCQ+2 / -02026
26Probability
The probability distribution of a random variable X is given by$X = x\(1\)2\(3\)4\(P(X = x)\)k\(2k\)3k$$4k$Then the c.d.f. of X is given by
MCQ+2 / -02026
27Probability
A random variable X has the probability distribution$X = x\(1\)2\(3\)4\(5\)6\(7\)8\(P(X = x)\)0.23\(0.15\)0.12\(0.10\)0.20\(0.07\)0.08$$0.05$for the events E = {X is a prime number} and F = {X $\leq$ 3}, then P (E$\cup$F)=
MCQ+2 / -02026
28Probability
Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the probability that the exactly two ships arrive safely is
MCQ+2 / -02026
29Probability
A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number.Let $p : P(A) = \dfrac{1}{3}$, $q$ : A and B are indep...
MCQ+2 / -02026
30Probability
If $E_1$ and $E_2$ are equally likely, mutually exclusive and exhaustive events and $P(A|E_1) = 0.2$, $P(A|E_2) = 0.3$, then $P(E_1|A)$ equal to...
MCQ+2 / -02026
31Probability
If a random variable $X$ has a probability mass function $P(x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3, 4 \\ 0, & \text{otherwise} \end{cases}$, then the mean of $X$ is ...
MCQ+2 / -02026
32Probability
If a fair coin is tossed 8 times, then the probability of getting at most 2 heads is...
MCQ+2 / -02026
33Probability
If A and B are two events such that $P(A) = \dfrac{2}{3}$, $P(B) = \dfrac{1}{2}$ and $P(A \mid B) = \dfrac{2}{3}$, then $P(A' \cup B) + P(A \cup B') = $
MCQ+2 / -02026
34Probability
The Variance of the following probability distribution of X isX$0\(1\)2\(3$P(X)$q^3\)3q^2 p\(3qp^2\)p^3$where $0 < p < 1, q = 1 - p$
MCQ+2 / -02026
35Probability
The centers for disease control have determined that when a person is given a vaccine, the probability that the person will develop immunity to a virus is $0.8$. If $8$ people are given this vaccine, then the probability that exactly $4$ wi...
MCQ+2 / -02026
36Probability
The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least once is.......
MCQ+2 / -02026
37Probability
A random variable X has the following probability distributionX12345678P(X=$x$)0.150.230.120.100.200.080.070.05For the event E = { X is a prime number } and F = { X < 4 }, P(E$\cup$F) =
MCQ+2 / -02026
38Probability
For the following probability distribution, the standard deviation of the random variable X isX234p(X=$x$)0.20.50.3
MCQ+2 / -02026
39Probability
If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is
MCQ+2 / -02026
40Probability
Let $X \sim B\left(6, \dfrac{1}{2}\right)$. Then the maximum probability occurs at
MCQ+2 / -02026
41Probability
A random variable 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
MCQ+2 / -02026
42Probability
A random variable X has the following probability distribution$X = x\(1\)2\(3\)4\(5\)6\(7\)8\(P(X=x)\)0.15\(0.23\)0.10\(0.12\)0.20\(0.08\)0.07$$0.05$For the events $E = \{X \text{ is a prime number}\}$, $F = \{X < 4\}$, $P(E \cup F)$ is
MCQ+2 / -02026
43Probability
The odds in favour of A winning a game of table tennis against B are 1:2. If 3 games are to be played, then the probability of A winning at least two games out of the three is.....
MCQ+2 / -02026
44Probability
A certain disease has a prevalence of $1\%$ in the population. A diagnostic test for the disease has a sensitivity of $98\%$ and a specificity of $95\%$. If a person from this population tests positive, then the probability that they actual...
MCQ+2 / -02026
45Probability
It is known that a box of $8$ batteries contains $3$ defective pieces and a person randomly selects $2$ batteries from this box. Then the probability distribution of the number of defective batteries is
MCQ+2 / -02026
46Probability
In a multiple-choice examination, there are $10$ questions with one correct option out of $4$ options for each question. A student gets $4$ marks for each correct answer and $1$ mark is deducted for each incorrect answer. The probability th...
MCQ+2 / -02026
47Probability
Two cards are drawn at random from a standard pack of $52$ cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...
MCQ+2 / -02026
48Probability
If the following function is probability density function of r.v. X$f(x) = kx^2(1-x)$, for $0 < x < 1 = 0$, otherwise, then the value of $k$ is
MCQ+2 / -02026
49Probability
Let $X \sim B(n, p)$. If $E(X) = 2$ and $\text{Var}(X) = 1$, then the probability of getting at most one success is .....
MCQ+2 / -02026
50Probability
If events A and B are such that $P(A) = \dfrac{1}{4}$, $P(A \cap B) = \dfrac{1}{10}$ and $P(A/B) = 2P(B/A)$ then $P(B) = $...........
MCQ+2 / -02026