List of top Questions asked in AP EAPCET- 2025

If 3 squares are chosen at random from the 64 squares of a chessboard, then the probability that all of them lie along the same diagonal line 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 find \(P(A \cap \overline{B})\).
A problem in Algebra is given to two students A and B whose chances of solving it are \(\dfrac{2}{5}\) and \(\dfrac{3}{5}\) respectively. The probability that the problem is solved if both try independently is
An urn A contains 4 white and 1 black ball; urn B contains 3 white and 2 black balls; urn C contains 2 white and 3 black balls. One ball is transferred randomly from A to B; then one ball is transferred randomly from B to C. Finally, a ball is drawn randomly from C. Find the probability that it is black.
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 black and one is red, is
A bag contains 5 red, 4 blue, and 3 green balls. Three balls are drawn at random. What is the probability that at least two balls are of the same color?
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 boys is
The mean and variance of a binomial distribution are \(x\) and \(5\) respectively. If \(x\) is an integer, then the possible values for \(x\) are
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 at least one correct pair of shoes among the four shoes drawn is:
A manufacturing company has 3 units A, B, and C which produce 25%, 35%, 40% of bulbs respectively. 5%, 4%, and 2% of their production is defective. If a bulb is found defective, the probability it came from B is
A box contains 5 defective and 15 non-defective bulbs. Two bulbs are drawn at random without replacement. What is the probability that at least one bulb is defective?
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 it is draw is 0.1. If they played three games, then the probability that A wins at least two games is

If the probability distribution of a random variable $X$ is as follows, then $P(X \leq 2) =$ 

A bag contains 5 balls of unknown colors. There are equal chances that out of these five balls, there may be 0 or 1 or 2 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 the only red ball in the bag 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 student is found to be asleep on an evening, the probability that he watched the TV is:
A bag contains 3 red and 4 blue balls. If one ball is drawn at random, what is the probability that it is red?
A and B are two independent events of a random experiment and \(P(A)>P(B)\). If the probability that both A and B occur is \(\frac{1}{6}\) and neither of them occurs is \(\frac{1}{3}\), then the probability of the occurrence of B is:
For three events \( A, B, \) and \( C \) of a sample space, if \[ P(\text{exactly one of A or B occurs}) = P(\text{exactly one of B or C occurs}) = P(\text{exactly one of C or A occurs}) = \frac{1}{4} \] and the probability that all three events occur simultaneously is \( \frac{1}{16} \), then the probability that at least one of the events occurs is
If 3 squares are chosen at random from the 64 squares of a chessboard, then the probability that all of them lie along the same diagonal line is:
An unbiased coin is tossed 8 times. The probability that head appears consecutively at least 5 times is
A family consists of 8 persons. If 4 persons are chosen at random and they are found to be 2 men and 2 women, then the probability that there are equal numbers of men and women in that family is:
Three letters are chosen at random from the letters of the word VARIABLE and all possible three-letter words (with or without meaning) are formed with them. Then the probability of getting a three-letter word having a consonant as its middle letter is:
Let \( X \) be the random variable taking values \( 1, 2, \dots, n \) 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:
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 \(P(A/B) =\)

The following data represents the frequency distribution of 20 observations: 

Then its mean deviation about the mean is: