List of top Mathematics Questions on Probability asked in KEAM

A biased die is rolled such that the probability of getting k dots,1≤k≤6, on the upper face of the die is proportional to k. Then the probability that five dots appear on the upper face of the die is 

Let the probability distribution of random variable X be

X	-2	-1	1	2	3
P(X=x)	k	2k	2k	k	3k

Then, the value of E(X²) is

A box contains 100 tickets numbered 00,01,02,....99 and a ticket is drawn at random. Let X denote the sum of the digits on that ticket and Y denote the product of those digits. Then the value of P(X=2IY=0) is

An electric bulb manufacturing company manufactures three types of electric bulbs A, B and C. In a room containing these three types of electric bulbs, it is known that 6% of type A electric bulbs are defective, 4% of type B electric bulbs are defective and 2% of type C electric bulbs are defective. An electric bulb is selected at random from a lot containing 50 type A electric bulbs,30 type B electric bulbs and 20 type C electric bulbs. The selected electric bulb is found to be defective. Then the probability that the selected electric bulb was type A is

Let Ω={1,2,3,4,5}be the sample space with the events A={1,2,5},B={1,3,5} and c={2,3,5}.Let E^c denote the complement of an event E.Then P((A∩B)^c∪C^c) is

A box contains 10 coupons, labelled as 1,2,.....10.Three coupons are drawn at random and without  X1,X2 and X3 denote the numbers on the coupons. Then the probability that max{X1,X2,X3}<7 is 

Let \(X\) be a random variable following Binomial distribution B in(\(n.p\)),where n is the number of independent Bernoulli trials and \(p\) is the probability of success. If \(E(X)=1\) and \(Var(X)=\dfrac{4}{5}\) ,then the values of \(n\) and \(p\) are

Consider two independent events \(E\) and \(F\) such that\( P(E)=1/4,P(E∪F)=2/5\) and \(P(F)=a\).Then,the value of \(a\) is

A coin is tossed thrice. The probability of getting a head on the second toss given that a tail has occurred in at least two tosses is 

There are two cash counters A and B for placing orders in a college canteen. Let \(EA\) be the event that there is a queue at counter A and \(EB\) denotes the event that there is a queue at counter B. If \(P(EA)=0.45\) ,\(P(EB)=0.55\) and \(P(EA∩EB)=0.25\),then the probability that there is no queue at both the counters is:

A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome is 

Let A and B be two independent events such that the odds in favour of A and B are \(1:1 \) and \(3:2\) respectively .Then the probability that only one of the two occurs is 

An urn contains 8 black marbles and 4 white marbles. Two marbles are chosen at random and without replacement. Then the probability that both marbles are black is 

There are 4 red, 3 blue and 3 yellow marbles in an urn. If three marbles are drawn simultaneously, then the probability that the number of yellow marbles will be less than 2 is equal to

Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that min(a, b, c) =6 is

In a box there are four marbles and each of them is marked with distinct number from the set {1, 2, 5, 10}. If one marble is randomly selected four times with replacement and the number on it noted, then the probability that the sum of numbers equals 18 is

If A and B are two events such that P(A)=0.5, P(B)=0.4 and P(A\(\cap\)B)=0.2, then P(A|(A\(\cup\)B)) is equal to

There are 37 men and 33 women at a party. If a prize is given to one person chosen at random, then the probability that the prize goes to a woman is

A fair coin is tossed twice. Given that the first toss resulted in head, then the probability that the second toss also, would result in head is

A covid-19 vaccination reduces the probability of getting covid-19 infection from 0.4 to 0.1. In a city, 45% people are vaccinated. Then the probability that a non-vaccinated person chosen at random in the city gets covid-19 infection is

If A and B are two events such that P(A) = 0.2, P(B) = 0.55 and P(A∩B)=0.1, then P(B∩A^c) is equal to

Two dice are rolled. If A is the event that sum of the numbers is 4 and B is the event that at least one of the dice shows a 3, then P(A|B) is equal to

A bag contains 5 yellow, 3 green, 2 blue and 7 white balls. If 4 balls are chosen at random, then the probability that none of them are white is

An urn contains 25 marbles which are numbered from 1 to 25 and a marble is chosen at random two times with replacement. Then the probability that both times the marble has the same number is