# Probability · Mathematics · MHT CET

Start Practice## MCQ (Single Correct Answer)

MHT CET 2023 14th May Evening Shift

A fair die with numbers 1 to 6 on their faces is thrown. Let $$\mathrm{X}$$ denote the number of factors of the number, on the uppermost face, then th...

MHT CET 2023 14th May Evening Shift

The p.m.f. of a random variable $$\mathrm{X}$$ is $$\mathrm{P}(x)=\left\{\begin{array}{cl}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \mat...

MHT CET 2023 14th May Evening Shift

There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the probability, that the product is a ...

MHT CET 2023 14th May Evening Shift

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that...

MHT CET 2023 14th May Morning Shift

Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

MHT CET 2023 14th May Morning Shift

For an initial screening of an entrance exam, a candidate is given fifty problems to solve. If the probability that the candidate can solve any proble...

MHT CET 2023 14th May Morning Shift

$$\text { If } f(x)= \begin{cases}3\left(1-2 x^2\right) & ; 0...

MHT CET 2023 14th May Morning Shift

Three critics review a book. For the three critics the odds in favour of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respectively. The probability that t...

MHT CET 2023 13th May Evening Shift

Two dice are rolled. If both dice have six faces numbered $$1,2,3,5,7,11$$, then the probability that the sum of the numbers on upper most face is pri...

MHT CET 2023 13th May Evening Shift

A random variable $$X$$ has the probability distribution
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MHT CET 2023 13th May Morning Shift

A random variable $$X$$ has the following probability distribution
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MHT CET 2023 13th May Morning Shift

Let $$\mathrm{X}$$ be random variable having Binomial distribution $$B(7, p)$$. If $$P[X=3]=5 P[X=4]$$, then variance of $$\mathrm{X}$$ is

MHT CET 2023 13th May Morning Shift

If a continuous random variable $$\mathrm{X}$$ has probability density function $$\mathrm{f}(x)$$ given by
$$f(x)=\left\{\begin{array}{cl}
a x & , \te...

MHT CET 2023 13th May Morning Shift

A card is drawn at random from a well shuffled pack of 52 cards. The probability that it is black card or face card is

MHT CET 2023 12th May Evening Shift

An irregular six faced die is thrown and the probability that, in 5 throws it will give 3 even numbers is twice the probability that it will give 2 ev...

MHT CET 2023 12th May Evening Shift

A box contains 100 tickets numbered 1 to 100 . A ticket is drawn at random from the box. Then the probability, that number on the ticket is a perfect ...

MHT CET 2023 12th May Evening Shift

Three fair coins with faces numbered 1 and 0 are tossed simultaneously. Then variance (X) of the probability distribution of random variable $$\mathrm...

MHT CET 2023 12th May Morning Shift

The p.m.f of random variate $$\mathrm{X}$$ is $$P(X)= \begin{cases}\frac{2 x}{\mathrm{n}(\mathrm{n}+1)}, & x=1,2,3, \ldots \ldots, \mathrm{n} \\ 0, & ...

MHT CET 2023 12th May Morning Shift

An experiment succeeds twice as often as it fails. Then the probability, that in the next 6 trials there will be atleast 4 successes, is

MHT CET 2023 12th May Morning Shift

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks is...

MHT CET 2023 12th May Morning Shift

$$\mathrm{A}$$ and $$\mathrm{B}$$ are independent events with $$\mathrm{P}(\mathrm{A})=\frac{1}{4}$$ and $$\mathrm{P}(\mathrm{A} \cup \mathrm{B})=2 \m...

MHT CET 2023 11th May Evening Shift

Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Then mean of number of tens is

MHT CET 2023 11th May Evening Shift

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of fours in two tosses, then the probability distribution of $$\mathrm{...

MHT CET 2023 11th May Evening Shift

If $$\mathrm{A}$$ and $$\mathrm{B}$$ are two events such that $$\mathrm{P}(\mathrm{A})=\frac{1}{3}, \mathrm{P}(\mathrm{B})=\frac{1}{5}, \mathrm{P}(\ma...

MHT CET 2023 11th May Evening Shift

Let a random variable $$\mathrm{X}$$ have a Binomial distribution with mean 8 and variance 4. If $$\mathrm{P}(\mathrm{X} \leq 2)=\frac{\mathrm{K}}{2^{...

MHT CET 2023 11th May Morning Shift

From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one without replacement. The expected va...

MHT CET 2023 11th May Morning Shift

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals __...

MHT CET 2023 11th May Morning Shift

A binomial random variable $$\mathrm{X}$$ satisfies $$9. p(X=4)=p(X=2)$$ when $$n=6$$. Then $$p$$ is equal to

MHT CET 2023 10th May Evening Shift

The three ships namely A, B and C sail from India to Africa. If the odds in favour of the ships reaching safely are $$2: 5,3: 7$$ and $$6: 11$$ respec...

MHT CET 2023 10th May Evening Shift

If the sum of mean and variance of a Binomial Distribution is $$\frac{15}{2}$$ for 10 trials, then the variance is

MHT CET 2023 10th May Evening Shift

In a game, 3 coins are tossed. A person is paid ₹ 7 /-, if he gets all heads or all tails; and he is supposed to pay ₹ 3 /-, if he gets one head or tw...

MHT CET 2023 10th May Evening Shift

A fair die is tossed twice in succession. If $$\mathrm{X}$$ denotes the number of sixes in two tosses, then the probability distribution of $$\mathrm{...

MHT CET 2023 10th May Morning Shift

For a binomial variate $$\mathrm{X}$$ with $$\mathrm{n}=6$$ if $$P(X=4)=\frac{135}{2^{12}}$$, then its variance is

MHT CET 2023 10th May Morning Shift

The p.d.f. of a discrete random variable is defined as
$$\mathrm{f}(x)=\left\{\begin{array}{l}
\mathrm{k} x^2, 0 \leq x \leq 6 \\
0, \text { otherwise...

MHT CET 2023 10th May Morning Shift

A player tosses 2 fair coins. He wins ₹5 if 2 heads appear, ₹ 2 if one head appears and ₹ 1 if no head appears. Then the variance of his winning amoun...

MHT CET 2023 10th May Morning Shift

Three critics review a book. For the three critics the odds in favor of the book are $$2: 5, 3: 4$$ and $$4: 3$$ respectively. The probability that th...

MHT CET 2023 9th May Evening Shift

A man takes a step forward with probability 0.4 and backwards with probability 0.6 . The probability that at the end of eleven steps, he is one step a...

MHT CET 2023 9th May Evening Shift

A problem in statistics is given to three students A, B and C. Their probabilities of solving the problem are $$\frac{1}{2}, \frac{1}{3}$$ and $$\frac...

MHT CET 2023 9th May Evening Shift

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards, then mean of number of queens is

MHT CET 2023 9th May Morning Shift

In a Binomial distribution with $$\mathrm{n}=4$$, if $$2 \mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=2)$$, then the variance is

MHT CET 2023 9th May Morning Shift

$$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ are three events, one of which must and only one can happen. The odds in favor of $$\mathrm{A}$$ are $$4: 6$$, ...

MHT CET 2023 9th May Morning Shift

The probability mass function of random variable X is given by
$$P[X=r]=\left\{\begin{array}{ll}
\frac{{ }^n C_r}{32}, & n, r \in \mathbb{N} \\
0, & ...

MHT CET 2023 9th May Morning Shift

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable $$\mathrm{X}$$, ...

MHT CET 2022 11th August Evening Shift

The incidence of occupational disease in an industry is such that the workmen have a $$10 \%$$ chance of suffering from it. The probability that out o...

MHT CET 2022 11th August Evening Shift

If $$P(A \cup B)=0.7, P(A \cap B)=0.2$$, then $$P\left(A^{\prime}\right)+P\left(B^{\prime}\right)$$ is

MHT CET 2022 11th August Evening Shift

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

MHT CET 2021 24th September Evening Shift

The probability that at least one of the events $$E_1$$ and $$E_2$$ occurs is 0.6. If the simultaneous occurrence of $$\mathrm{E}_1$$ and $$\mathrm{E}...

MHT CET 2021 24th September Evening Shift

Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is

MHT CET 2021 24th September Evening Shift

The probability distribution of a random variable X is
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MHT CET 2021 24th September Evening Shift

A fair coin is tossed for a fixed number of times. If probability of getting 7 heads is equal to probability of getting 9 heads, then probability of g...

MHT CET 2021 24th September Morning Shift

If the probability distribution function of a random variable X is given as
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MHT CET 2021 24th September Morning Shift

If $$\mathrm{P}(\mathrm{A})=\frac{3}{10}, \mathrm{P}(\mathrm{B})=\frac{2}{5}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{3}{5}$$, then $$\mathrm{P}(...

MHT CET 2021 24th September Morning Shift

The probability distribution of a discrete random variable X is
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MHT CET 2021 24th September Morning Shift

A die is thrown four times. The probability of getting perfect square in at least one throw is

MHT CET 2021 23rd September Evening Shift

A man is known to speck truth 3 out of 4 times. He throws a die and reports that it is 6. Then the probability that it is actually 6 is

MHT CET 2021 23rd September Evening Shift

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on
one face is

MHT CET 2021 23rd September Evening Shift

Let two cards are drawn at random from a pack of 52 playing cards. Let X be the number of aces obtained. Then the value of E(X) is

MHT CET 2021 23rd September Evening Shift

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

MHT CET 2021 23rd September Evening Shift

If the function defined by $$f(x)=K(x-x^2)$$ if $$0 ...

MHT CET 2021 23th September Morning Shift

The probability distribution of the number of doublets in four throws of
a pair of dice is given by

MHT CET 2021 23th September Morning Shift

For the probability distribution given by following
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MHT CET 2021 23th September Morning Shift

A random variable X has the following probability distribution
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MHT CET 2021 23th September Morning Shift

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime...

MHT CET 2021 22th September Evening Shift

The distribution function $$F(X)$$ of discrete random variable $$X$$ is given by
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MHT CET 2021 22th September Evening Shift

First bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one ba...

MHT CET 2021 22th September Evening Shift

A fair coin is tossed 4 times. If $$X$$ is a random variable which indicates number of heads, then $$\mathrm{P}[\mathrm{X}

MHT CET 2021 22th September Evening Shift

If the mean and variance of a binomial distribution are 4 and 2 respectively, then probability of getting 2 heads is

MHT CET 2021 22th September Morning Shift

For two events $$\mathrm{A}$$ and $$\mathrm{B}, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{5}{6}, \mathrm{P}(\mathrm{A})=\frac{1}{6}, \mathrm{P}(\ma...

MHT CET 2021 22th September Morning Shift

A random variable X has following distribution
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MHT CET 2021 22th September Morning Shift

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails, then P (X = 1) =

MHT CET 2021 22th September Morning Shift

A random variable X $$\sim$$ B (n, p), if values of mean and variance of X are 18 and 12 respectively, then n =

MHT CET 2021 21th September Evening Shift

an urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. The probability that the three b...

MHT CET 2021 21th September Evening Shift

It is observed that $$25 \%$$ of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the pr...

MHT CET 2021 21th September Morning Shift

In a meeting $$60 \%$$ of the members favour and $$40 \%$$ oppose a certain proposal. A member is selected at random and we take $$\mathrm{X}=0$$ if h...

MHT CET 2021 21th September Morning Shift

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retain store, then the probability that the sto...

MHT CET 2021 21th September Morning Shift

A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both, is

MHT CET 2021 21th September Morning Shift

If $$\mathrm{X}$$ is a random variable with p.m.f. as follows.
$$\begin{aligned}
\mathrm{P}(\mathrm{X}=\mathrm{x}) & =\frac{5}{16}, \mathrm{x}=0,1 \\
...

MHT CET 2021 20th September Evening Shift

The p.m.f. of a random variable X is $$\mathrm{P(X = x) = {1 \over {{2^5}}}\left( {_x^5} \right),x = 0,1,2,3,4,5}=0$$ then

MHT CET 2021 20th September Evening Shift

The variance of the following probability distribution is,
...

MHT CET 2021 20th September Evening Shift

If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is

MHT CET 2021 20th September Evening Shift

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is

MHT CET 2021 20th September Morning Shift

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is

MHT CET 2021 20th September Morning Shift

A random variable X has the following probability distribution
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MHT CET 2021 20th September Morning Shift

Rajesh has just bought a VCR from Maharashtra Electronics and the shop offers after sales service contract for Rs. 1000 for the next five years. Consi...

MHT CET 2021 20th September Morning Shift

If $$X \sim B(4, p)$$ and $$P(X=0)=\frac{16}{81}$$, then $$P(X=4)=$$

MHT CET 2020 19th October Evening Shift

The odds in favour of getting sum multiple of 3 , when pair of dice are thrown is

MHT CET 2020 19th October Evening Shift

If $X$ is a.r.v. with c.d.f $F(x)$ and its probability distribution is given by
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MHT CET 2020 16th October Evening Shift

The odds in favour of drawing a king from a pack of 52 playing cards is

MHT CET 2020 16th October Evening Shift

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one pe...

MHT CET 2020 16th October Evening Shift

The pdf of a continuous r.v. $$X$$ is given by $$f(x)=\frac{x}{8}, 0

MHT CET 2020 16th October Evening Shift

If a die is thrown at random, then the expectation of the number on it is

MHT CET 2020 16th October Morning Shift

The probability that bomb will miss the target is 0.2. Then, the probability that out of 10 bombs dropped exactly 2 will hit the target is

MHT CET 2020 16th October Morning Shift

The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is

MHT CET 2020 16th October Morning Shift

The p.d.f of c.r.v $$X$$ is given by $$f(x)=\frac{x+2}{18}$$, if $$-2

MHT CET 2020 16th October Morning Shift

If the p.m.f of a. r.v. $$X$$ is given by
$$P(X=x)=\frac{{ }^5 C_x}{2^5}$$
if $$x=0,1,2, \ldots \ldots . .5=0$$,
0 , otherwise,
then which of the foll...

MHT CET 2019 3rd May Morning Shift

Let $X$ be the number of successes in ' $n$ ' independent Bernoulli trials with probability of success $p=\frac{3}{4}$. The least value of ' $n$ ' so ...

MHT CET 2019 3rd May Morning Shift

The probability that three cards drawn from a pack of 52 cards, all are red is

MHT CET 2019 3rd May Morning Shift

$$\begin{aligned}
&\text { The pdf of a random variable } X \text { is }\\
&\begin{aligned}
f(x) & =3\left(1-2 x^2\right), & & 0
The $P\left(\frac{1}{...

MHT CET 2019 3rd May Morning Shift

A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then variance of his winning amoun...

MHT CET 2019 2nd May Evening Shift

In a bionomial distribution, mean is 18 and variance is 12 then $p=$ ...........

MHT CET 2019 2nd May Evening Shift

The p.d.f of a random variable $x$ is given by
$$\begin{aligned}
& f(x)=\frac{1}{4 a}, \quad 00) \\
& =0 \text {, otherwise }
\end{aligned}$$
and $P\l...

MHT CET 2019 2nd May Evening Shift

If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is

MHT CET 2019 2nd May Morning Shift

It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the prob...

MHT CET 2019 2nd May Morning Shift

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is ...........

MHT CET 2019 2nd May Morning Shift

A random variable X has following probability distribution
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MHT CET 2019 2nd May Morning Shift

If the c.d.f (cumulative distribution function) is given by $F(x)=\frac{x-25}{10}$, then $P(27 \leq x \leq 33)=\ldots \ldots$