Probability PYQs - Last 10 Years

AP EAPCET / Mathematics / Algebra / 156 recent questions

MathematicsAlgebra2016-2025

All Probability PYQs Last 5 Years Create chapter test

Practice 156 AP EAPCET Mathematics questions from Probability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

156

PYQs on Page

Mathematics / Algebra

2021-2025

Year Range

Based on indexed question metadata

156

Last 5 Years

2021-2025

156

Last 10 Years

2016-2025

Recent Year Trend

2021

2022

2023

2024

2025

202157 max PYQs/year2025

Question Types

156PYQs

MCQ100%

Difficulty Mix

#1 Unknown156

156 in last 5 years156 in last 10 years

Last 10 Years Probability Questions

Showing 50 of 156 filtered questions.

$A$ bag $P$ contains 4 red and 5 black balls another bag Q contains 3 red and 6 black balls. If one ball is drawn at random from bag $P$ and two balls are drawn from bag $Q$, then the probability that out of the three balls drawn two are bl...

A radar system can detect an enemy plane in one out of ten consecutive scans.
The probability that it can detect an enemy plane atleast twice in four consecutive scans is

Let $X$ be the random variable taking values $1,2, \ldots n$ for a fixed positive integer $n$. If $P(X=k)=\frac{1}{n}$ for $1 \leq k \leq n$, then the variance of $X$ is

On every evening, a student either watches TV or reads a book. The probability of watching TV is $\frac{4}{5}$ If he watches TV, the probability that he will fall asleep is $\frac{3}{4}$ and it is $\frac{1}{4}$ when he reads a book. If the ...

For three events $A, B$ and $C$ of a sample space, $P$ (exactly one of $A$ or $B$ occurs ) $=P$ (exactly one of $B$ or $C$ occurs) $=P($ exactly one of $C$ or $A$ occurs $)=\frac{1}{4}$. If probability of all the three events occurring simu...

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is $\frac{1}{4}$ and the probability that the second student gets qualified in the same exam is $\frac{2}{5}$, t...

X denotes the number of times heads that occur in $n$ tosses of a fair coin. If $P(X=4), P(X=5)$ and $P(X=6)$ ate in arithmetic progression. The largest value of $n$ is

Two candidates $A$ and $B$ have attended an interview conducted by a recruitment board for two jobs, If the probability that candidate $A$ will get the job is 0.8 and the probability that candidate $B$ will get the job is 0.7 , then the pro...

The probability distribution of a random variable $X$ is as follows. Then, the mean of $x$ is

X
=
X

I
1

X
=
X

I
1

X=XI_(1)

P

(
X
=

X
i

)

P

...

All possible words (with or without meaning) are formed by taking atleast 2 letters (all different) from the letters of the word 'CURVE'. If a word is chosen at random from all the words thus formed, then the probability of getting $a$ lett...

If two events $A$ and $B$ are such that $P(\bar{A})=03, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, then $P(B / A \cup \bar{B})=$

Three numbers are chosen from 1 to 30 . The probability that they are not three consecutive numbers is

A family consists of 8 persons. If 4 persons are chosen a random and they are found to be 2 men and 2 women, then the probability that there are equal number of men and women in that family is

The number of trials conducted in a binomial distribution is 6 . If the difference between the mean and variance of this variate is $\frac{27}{8}$, then the probability of getting atmost 2 successes is

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than 8 as their sum, then $P(A \cap \bar{B})=$

$A$ and $B$ are two independent events of a random experiment and $P(A)>P(B)$.

If the probability that both $A$ and $B$ occurs is $\frac{1}{6}$ and neither of them occurs is $\frac{1}{3}$, then the probability of the occurance of $B$ is

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$, then $P(X \leq 3)=$

A company representative is distributing 5 identical samples of a product among 12 houses in a row such that each house gets at most one sample. The probability that no two consecutive house get one sample is

If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2)=$

In a school there are 3 sections $A, B$ and $C$. Section $A$ contains 20 girls and 30 boys, section $B$ contains 40 girls and 20 boys and section $C$ contains 10 girls and 30 boys. The probabilities of selecting the section $A, B$ and $C$ a...

If the probability distribution of a random variable $X$ is as follows, then the mean of $X$ is
$$ \begin{array}{ccccc} \hline \boldsymbol{X}=\boldsymbol{x}_{\boldsymbol{i}} & -1 & 0 & 1 & 2 \\ \hline \boldsymbol{P}\left(\boldsymbol{X}=\bol...

Two cards are drawn from a pack of 52 playing cards one after the other without replacement. If the first card drawn is a queen, then the probability of getting a face card from a black suit in the second draw is

A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. If one fruit is picked out at random from each basket, then the probability of getting one apple and one orange is

An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3 . The device gives accurate result in 8 out of 10 such tests.
If the device reports that an item tested is not defective, then the pr...

If 3 squares are chosen at random from the 64 squares of a chess board, then the probability that all of them lie along the same diagonal line is

If the average number of accidents occurring at a particular junction on a highway in a week is 5 , then the probability that atmost one accident occurs in a particular week is

The probability distribution of a discrete random variable $X$ is given below
$$ \begin{array}{lllll} \hline X=x & -1 & 0 & 1 & 2 \\ \hline P(X=x) & \frac{1}{3} & \frac{1}{6} & \frac{1}{6} & \frac{1}{3} \\ \hline \end{array} $$
Then, the va...

In a shoe rack there are 4 pairs of shoes and 4 shoes. are drawn one after the other at random without replacement. Then, the probability of getting atleast one correct pair of shoes among the four shoes drawn is

A rational number is selected at random from the distinct rational numbers of the form $p / q$ formed with $p$ and $q$ belonging to the set $\{1,2,3,4,5,6\}$. The probability that the rational number selected is a proper fraction, is

A bag contains 5 balls of unknown colours. There are equal chances that out of these five balls, there may be 0 or 12 or or 3 or 4 or 5 red balls, A ball is taken out from the bag at random and is found to be red. The probability that it is...

A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, then the probability that it contains atleast one woman is

If $X \sim B(9, p)$ is a binomial variate satisfying the equation $P(X=3)=P(X=6)$, then $P(X<3)=$

There are 8 boys and 7 girls in a class room. If the names of all those children are written on paper slips and 3 slips are drawn at random from them, then the probability of getting the names of one boy and two girls or one girl and two bo...

A die is thrown twice. Let A be the event of getting a prime number when the die is thrown first time and $B$ be the event of getting an even number when the die is thrown second time. Then, $P(A / \bar{B})=$

If $X$ follows poisson distribution with variance 2 , then $P(X \geq 3)=$

$U_1, U_2, U_3$ are three urns. $U_1$ contains 5 red, 3 white, 2 back balls: $U_2$ contains 4 red 4 white, 2 black balls and $U_3$ contains 3 red. 4 white, 3 black balls. If a ball is chosen at random from an urn chosen at random, then the ...

$A$ and $B$ are playing chess game with each other. The probability that $A$ wins the game is 0.6 . the probability that he loses is 0.3 and the probability its draw is 0.1 . If they played three games, then the probability that $A$ wins at...

If $l, m$ represent any two elements (identical or different) of the set $\{1,2,3,4,5,6,7\}$, then the probability that $l x^2+m x+1>0 \forall x \in R$ is

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person
$B$ completes the same work in the same time is $\frac{3}{4}$.
If both $A$ and $B$ start doing this work at the same...

If the probability distribution of a random variable $X$ is as follows, then $P(X \leq 2)=$
$$ \begin{array}{cccccc}\hline x_i & 0 & 1 & 2 & 3 & 4 \\ \hline P\left(X=x_i\right) & 3 k & 5 k & 3 k^2 & 4 k^2+k & 3 k^2 \\ \hline \end{array} $$

In a binomial distribution, if $n=4$ and $P(X=0)=\frac{16}{81}$, then $P(X=4)=$

If the probability distribution of a discrete random variable $X$ is given by
$P(X=k)=\frac{2^{-k}(3 k+1)}{2^c}, k=0,1,2, \ldots \ldots \infty$, then $P(X \leq c)=$

An urn $A$ contains 4 white and 1 black ball; urn $B$ contains 3 white and 2 black balls and urn $C$ contains 2 white and 3 black balls. One ball is transferred randomly from $A$ to $B$; later one ball is transferred randomly from $B$ to $C...

There are three families $F_1, F_2, F_3 . F_1$ has 2 boys and 1 girl; $F_2$ has 1 boy and 2 girls; $F_3$ has 1 boy and 1 girl. A family is randomly chosen and a child is chosen from that family randomly. If it is known that the child thus s...

A box contains twelve balls of which 4 are red, 5 are green and 3 are white. If three balls are drawn at random simultaneously from the box, then the probability that exactly 2 balls have the same colour is

An unbiased coin is tossed 8 times. The probability that head appears consecutively at least 5 times is

The probability that a student gets distinction in a Mathematics test is $\frac{2}{3}$. If five such tests are conducted over a certain period of time, then the probability that he gets distinction in atleast 3 tests is

A manufacturing company of bulbs has 3 units $A, B$ and $C$ which produce $25 \%, 35 \%$ and $40 \%$ of the bulbs respectively. Out of the bulbs produced by $A, B, C$ units, $5 \%, 4 \%$ and $2 \%$ are defective, respectively. If a bulb is ...

Three dice are thrown simultaneously and the sum of the numbers appeared on them is noted. If $A$ is the event of getting a sum greater than 14 and $B$ is the event of getting a sum which is a multiple of 3 , then $P(A \cap \bar{B})+P(\bar{...

A problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively.
The probability that the problem is solved if both of them try independently is