Probability PYQs - Last 5 Years

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Practice 214 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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Last 5 Years Probability Questions

Showing 50 of 214 filtered questions.

The probability mass function of a random variable X is given by$P(X = x) = \dfrac{{}^{5}C_x}{2^5}$, for $x = 0, 1, 2, 3, 4, 5$ and $= 0$, otherwise.Then which of the following is correct?

A player tosses two fair coins, he wins Rs. $5$ if two heads appear, Rs. $3$ if one head appears and Rs. $2$ if no head appears, then the variance of the winning amount is

If $X \sim B(n, p)$, then the value of $\dfrac{P(X = k)}{P(X = k - 1)}$ is

A student studies for X number of hours during a randomly selected school day. The probability that X can take the values, has the following form, where k is some constant.
$$ \mathrm{P}(\mathrm{X}=x)= \begin{cases}0.2, & \text { if } x=0 \...

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

Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then $\mathrm{E}\left(\mathrm{X}^2\right)=$

If $\mathrm{X} \sim \mathrm{B}(35, \mathrm{p})$ such that $7 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$ then the value of $\frac{\mathrm{P}(\mathrm{X}=15)}{\mathrm{P}(\mathrm{X}=20)}$ is equal to

A box contains 8 red and $x$ number of green balls. 3 balls are drawn at random, if the probability that 3 balls being red is $\frac{7}{15}$, then number of green balls is…

The cumulative distribution function of a discrete random variable X is
$$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 & 0.85 ...

The probability that a person is not a sportsperson is $\frac{1}{6}$. Then the probability that out of the 6 members of the family, 5 are sportspersons is

The following is p.d.f. of continuous random variable X
$$ \mathrm{f}(x)= \begin{cases}\frac{x}{8} & , \text { if } 0 < x < 4 \\ 0 & , \text { otherwise }\end{cases} $$
Then $F(0.5), F(1.7)$ and $F(5)$ is respectively

A fair coin is tossed a fixed number of times. If the probability of getting 5 tails is same as the probability of getting 7 tails, then the probability of getting 3 tails is

A fair $n$ faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$, then $\mathrm{n}=($ where $\mathrm{n} \in \mathbb{N})$

The probability that a non leap year selected at random will contain 52 Saturdays or 53 Sundays is

Let X denote the number of hours you study on a Sunday. It is known that
$$ \mathrm{P}(\mathrm{X}=x)=\left\{\begin{array}{cc} 0.1 & , \text { if } x=0 \\ \mathrm{k} x & , \text { if } x=1 \text { or } 2 \\ \mathrm{k}(5-x) & , \text { if } x...

A family has 3 children. The probability that all the three children are girls, given that at least one of them is a girl is

A pair of fair dice is thrown 4 times. If getting the same number on both dice is considered as a success, then the probability of two successes are

If a random variable X has the following probability distribution of X
$$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \mathrm{P}(\mathrm{X}=x) & 0 & \mathrm{k} & 2 \mathrm{k} & 2 \mathrm{...

The probability that a student is not a swimmer is $\frac{1}{5}$. The probability that out of 5 students selected at random 4 are swimmers is

A player tosses two coins. He wins ₹ 10 , if 2 heads appears, ₹ 5 , if one head appear and ₹ 2 if no head appears. Then variance of winning amount is

A doctor assumes that patient has one of three diseases $\mathrm{d} 1, \mathrm{~d} 2$ or d 3 . Before any test he assumes an equal probability for each disease. He carries out a test that will be positive with probability 0.7 if the patient...

Consider the probability distribution
$$ \begin{array}{|l|l|l|l|l|l|} \hline \mathrm{X}=x & 1 & 2 & 3 & 4 & 5 \\ \hline \mathrm{P}(\mathrm{X}=x) & \mathrm{K} & 2 \mathrm{~K} & \mathrm{~K}^2 & 2 \mathrm{~K} & 5 \mathrm{~K}^2 \\ \hline \end{a...

Bag I contains 3 red and 2 green balls and Bag II contains 5 red and 3 green balls. A ball is drawn from one of the bag at random and it is found to be green. Then the probability that it is drawn from Bag I is

In a game a man wins $Rs \,\, 40$ if he gets 5 or 6 on a throw of a fair die and loses ₹ 20 for getting any other number on the die. If he decides to throw the die either till he gets a five or six or to a maximum of three throws, then his ...

A fair coin is tossed 100 times. The chance of getting a head even number of times is

A random variable X has following p.d.f. $\mathrm{f}(x)=\mathrm{kx}(1-x), 0 \leqslant x \leqslant 1 \quad$ and $\quad \mathrm{P}(x>\mathrm{a})=\frac{20}{27}$, then $\mathrm{a}=$

If A and B are independent events such that $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}^{\prime}\right)=\frac{3}{25}$ and $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)=\frac{8}{25}$, then $P(A)=$

If $X \sim B\left(6, \frac{1}{2}\right)$, then $P(|X-2| \leqslant 1)=$

The probability that a certain kind of component will survive a given test is $\frac{2}{3}$. The probability that at most 2 components out of 4 tested, will survive is

A coin is tossed until one head appears or a tail appears 4 times in succession. The probability distribution of the number of tosses is

The p.d.f. of a continuous random variable X is $f(x)=\left\{\begin{array}{cl}\frac{x^2}{18} & , \text { if }-3 < x < 3 \\ 0 & \text { otherwise }\end{array}\right.$
Then $\mathrm{P}[|\mathrm{X}|<2]=$

In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

In a box containing 100 apples, 10 are defective. The probability that in a sample of 6 apples, 3 are defective is

Three urns respectively contain 2 white and 3 black, 3 white and 2 black and 1 white and 4 black balls. If one ball is drawn from each um, then the probability that the selection contains 1 black and 2 white balls is

If a random variable $X$ has p.d.f. $f(x)=\left\{\begin{array}{ll}\frac{a x^2}{2}+b x & , \text { if } 1 \leqslant x \leqslant 3 \\ 0 & , \text { otherwise }\end{array}\right.$ and $f(2)=2$, then the values of $a$ and $b$ are, respectively

The probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two 'I's do not come together is

If a random variable X follows the Binomial distribution $B(10, \quad p)$ such that $5 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$, then the value of $\frac{\mathrm{P}(\mathrm{X}=5)}{\mathrm{P}(\mathrm{X}=6)}$ is equal to

A random variable X takes values $0,1,2,3$, ........ with probabilities. $\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1)\left(\frac{1}{2}\right)^x, \mathrm{k}$ is a constant, then $P(X=1)=$

The following is the probability distribution of X
$$ \begin{array}{|c|c|c|c|c|} \hline \mathrm{X} & 0 & 1 & 2 & 3 \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1+\mathrm{p}}{5} & \frac{2-2 \mathrm{p}}{5} & \frac{2-\mathrm{p}}{5} & \frac{2 \ma...

If $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are mutually exclusive and exhaustive events of a sample space $S$ such that $P(B)=\frac{3}{2} P(A)$ and $P(C)=\frac{1}{2} P(B)$, then $P(A)=$

A random variable, $X$ has p.m.f. $\mathrm{P}(\mathrm{X}=x)=\frac{{ }^4 \mathrm{C}_x}{2^4}, x=0,1,2,3,4$ and $\mu$ and $\sigma^2$ are mean and variance respectively of random variable X , then

\(\text { The c.d.f. of a discrete random variable } \mathrm{X} \text { is }\)
$$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \mathrm{X} & -3 & -1 & 0 & 1 & 3 & 5 & 7 & 9 \\ \hline \mathrm{~F}(\mathrm{X}=x) & 0.1 & 0.3 & 0.5 & 0.65 & 0.75 &...

Numbers are selected at random, one at a time from the two-digit numbers $00,01,02,-------, 99$ with replacement. An event E occurs only if the product of the two digits of a selected number is 24. If four numbers are selected, then probabi...

A random variable $X$ has the following probability distribution
$$ \begin{array}{|l|c|c|c|c|c|} \hline \mathrm{X}: & 0 & 1 & 2 & 3 & 4 \\ \hline \mathrm{P}(\mathrm{X}): & \mathrm{k} & 2 \mathrm{k} & 4 \mathrm{k} & 2 \mathrm{k} & \mathrm{k}...

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of $2 E(X)+3 E\left(X^2\right)$ for the number of queens is

If X is a binomial variable with range $\{0,1,2,3,4\}$ and $\mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=4)$ then the parameter ' $p$ ' of the binomial distribution is

If two numbers $p$ and $q$ are chosen randomly from the set $\{1,2,3,4\}$, one by one, with replacement, then the probability of getting $\mathrm{p}^2 \geq 4 \mathrm{q}$ is

Two numbers are selected at random, without replacement from the first 6 positive integers. Let $X$ denote the larger of the two numbers. Then $\mathrm{E}(\mathrm{X})=$

For $\mathrm{k}=1,2,3$ the box $\mathrm{B}_{\mathrm{k}}$ contains k red balls and $(k+1)$ white balls. Let $P\left(B_1\right)=\frac{1}{2}, P\left(B_2\right)=\frac{1}{3}$ and $\mathrm{P}\left(\mathrm{B}_3\right)=\frac{1}{6} . \mathrm{A}$ box...