List of top Mathematics Questions on Probability asked in TS EAMCET

The probability distribution of a random variable \(X\) is given below. Then, the mean of \(X\) is 

\(X=x_i\)\(0\)\(1\)\(2\)
\(P(X=x_i)\)\(3k^2\)\(2k^2\)\(k^2+k\)

The variance of the following continuous frequency distribution is 

Class Interval\(0\!-\!10\)\(10\!-\!20\)\(20\!-\!30\)
Frequency\(3\)\(4\)\(3\)
If the difference of mean and variance of a binomial distribution \(B(n,p)\) is \(\dfrac{4}{7}\) and their product is \(\dfrac{20}{7}\), then \(P(X=1)=\)
Two persons A and B are playing a game of rolling 2 dice alternately. The person who first gets the sum of the numbers appearing on the dice as a prime number will win the game. If A starts the game, then the probability of B winning the game is
Three persons A, B and C planned to have a running race among themselves. If the probability that A wins the race is three times that of B and the probability that B wins the race is \(\dfrac32\) times that of C, then the difference in probabilities of A and C to win the race is
A dealer bought a fixed number of laptops from 3 different companies A, B and C. Among these laptops, \(28\%\) are bought from A, \(32\%\) are bought from B and \(40\%\) are bought from C. \(2.5\%\) of laptops bought from A, \(1.5\%\) bought from B and \(1\%\) bought from C are likely to be defective. If a customer found that the laptop bought by him is defective, then the probability that it was from B is
A card is drawn from 52 cards. If A = diamond, B = ace, probability that exactly one occurs is
If 2 coins are tossed and 2 dice are thrown, probability of getting at least 1 head and sum at least 9 is
If a 4-digit number is chosen from all possible 4-digit numbers, probability of getting exactly three odd digits and one even digit is
Let \[ S=\{2,3,5,7,11,13\} \] Consider all onto functions from \(S\) to \(S\). If function \(f\) is chosen randomly, probability that \[ f(3)>3f(2) \] is
The coefficient of variation for the following data is
Among every 8 units of a product, one is likely to be defective. If a consumer has ordered 5 units of that product, then the probability that atmost one unit is defective among them is \

The range of a discrete random variable X is\( \{1, 2, 3\}\) and the probabilities of its elements are given by \(P(X=1) = 3k^3\), \(P(X=2) = 2k^2\) and \(P(X=3) = 7-19k\). Then \(P(X=3) = \)}

An urn contains 7 red, 5 white and 3 black balls. Three balls are drawn randomly one after the other without replacement. If it is known that first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is
Let A and B be two events in a random experiment. If \( P(A \cap \overline{B}) = 0.1 \), \( P(\overline{A} \cap B) = 0.2 \) and \( P(B) = 0.5 \) then \( P(A \cap B) = \)
If two smallest squares are chosen at random on a chess board then the probability of getting these squares such that they do not have a side in common is
A typist claims that he prepares a typed page with typo errors of 1 per 10 pages. In a typing assignment of 40 pages, if the probability that the typo errors are at most 2 is p, then \(e^2 p =\)
Two persons A and B play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even, A will get \( \frac{1}{2} \) point and B will get \( \frac{1}{2} \) point. If the sum is odd, A will get one point and B will get no point. The arithmetic mean of the random variable of the number of points of A is
A, B are the events in a random experiment. If \( P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(A \cap B)=\frac{1}{4} \), then \( P(A^c | B^c) + P(A | B) = \)
A, B1, B2, B3 are the events in a random experiment. If \( P(B_1)=0.25, P(B_2)=0.30, P(B_3)=0.45 \), \( P(A|B_1)=0.05, P(A|B_2)=0.04, P(A|B_3)=0.03 \), then \( P(B_2|A) = \)
Let \( P = \begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \) be a matrix. Three elements of this matrix P are selected at random. A is the event of having the three elements whose sum is odd. B is the event of selecting the three elements which are in a row or column. Then \( P(A) + P(A|B) = \)
If the variance of the numbers \( 9, 15, 21, \dots, (6n+3) \) is P, then the variance of the first \( n \) even numbers is
If \( X \sim B(7, p) \) is a binomial variate and \( P(X=3) = P(X=5) \) then \( p = \)

The mean deviation from the median for the following data is

\( x_i \)298357
\( f_i \)531661
If three dice are thrown, then the mean of the sum of the numbers appearing on them is