List of top Mathematics Questions on Probability asked in AP EAMCET

In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is:
A box contains 20 percent defective bulbs. Five bulbs are randomly chosen. Find the probability that exactly 3 are defective.
Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is:
If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:
A student writes an exam with 8 true/false questions. He passes if he answers at least 6 correctly. Find the probability that he fails.
In a class consisting of 40 boys and 30 girls, 30% of the boys and 40% of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics is:
If 5 letters are to be placed in 5-addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope is:
If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any die is:
P, Q, and R try to hit the same target one after another. Their probabilities of hitting are \( \frac{2}{3}, \frac{3}{5}, \frac{5}{7} \) respectively. Find the probability that the target is hit by P or Q but not by R.
There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is:
It is given that in a random experiment, events A and B are such that \( P(A) = \frac{1}{4} ,P(A|B) = \frac{1}{2} \) and \( P(B|A) = \frac{2}{3} \). Then \( P(B) \) is:
When two dice are thrown, the probability of getting the sum of the values on them as 10 or 11 is:
The probability that A speaks truth is 75\% and the probability that B speaks truth is 80\%. The probability that they contradict each other when asked to speak on a fact is:
A and B throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. A wins if he throws 6 before B throws 7, and B wins if he throws 7 before A throws 6. If A begins, the probability of his winning is:
A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:

Let $E_1$ and $E_2$ be two independent events of a random experiment such that
$P(E_1) = \frac{1}{2}, \quad P(E_1 \cup E_2) = \frac{2}{3}$.
Then match the items of List-I with the items of List-II:

two independent events

The correct match is:

A manufacturing company noticed that 1% of its products are defective. If a dealer orders 300 items from this company, then the probability that the number of defective items is at most one is:
If a number is drawn at random from the set \( \{1, 3, 5, 7, \dots, 59\} \), then the probability that it lies in the interval in which the function \( f(x) = x^3 - 16x^2 + 20x - 5 \) is strictly decreasing is:
If each of the coefficients \( a, b, c \) in the equation \( ax^2 + bx + c = 0 \) is determined by throwing a die, then the probability that the equation will have equal roots, is:
A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from the first bag and two balls from the second bag at random, the probability that out of the three, two are black and one is red, is:
If 7 different balls are distributed among 4 different boxes, then the probability that the first box contains 3 balls is:

Out of the first 5 consecutive natural numbers, if two different numbers x and y are chosen at random, then the probability that x4- y4 is divisible by 5 is:

If two cards are drawn randomly from a pack of 52 playing cards, then the mean of the probability distribution of number of kings is:
A bag contains 2 white, 3 green, and 5 red balls. If three balls are drawn one after the other without replacement, then the probability that the last ball drawn was red is:
The probability that a person goes to college by car,\(\frac{1}{5}\) bus,\(\frac{2}{5}\) or train \(\frac{3}{5}\) is given. If he reaches college on time, find the probability he traveled by car.