List of top Mathematics Questions on Probability

A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For i = 1, 2, 3, let W_i, G_i and B_i denote the events that the ball drawn in the i^th draw is a white ball, green ball, and blue ball, respectively. If the probability \(P(W_1∩G_2∩B_3)=\frac{2}{5N}\) and the conditional probability \(P(B_3|W_1∩G_2)=\frac{2}{9}\), then N equals ________.

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is \(\frac{1}{2}\) . Also assume that the probability of the answer for a question being guessed, given that the student’s answer is correct, is \(\frac{1}{6}\) . Then the probability that the student knows the answer of a randomly chosen question is

Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that the points (x, P(X = x)), x = 0,1,2,3,4, lie on a fixed straight line in the xy -plane, and P(X = x) = 0 for all x ∈ R - {0,1,2,3,4}. If the mean of X is \(\frac{5}{2}\) , and the variance of X is α, then the value of 24α is ______.

An urn contains 15 red, 10 white, 60 orange balls, 15 green balls. 2 balls are taken with replacement. Find the probability 1 ball is red and the other ball is white.

Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:

A coin is biased so that a head is twice as likely as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

Given set = {1, 2, 3, ..., 50} one number is selected randomly from the set. Find the probability that number is multiple of 4 or 6 or 7.

Bag A contains 7 white balls & 3 red balls. Bag B contains 3 white balls & 2 red balls. A ball is chosen randomly & found to be red then find the probability that it is taken from bag A.

The probability that Ajay will not go to office is \(\frac{1}{5}\) and probability that Ajay and Vijay will not go to the office is \(\frac{2}{7}\), if their visits to office is independent of each other, then find the probability that Ajay will go to the office, but Vijay will not go, is

Let  \(X = \{ {(x,y) ∈ Z \times Z : \frac{x^2}{8} + \frac {y^2}{20} < 1 \,and \,\,y^2 < 5x} \}\). Three distinct points P, Q and R are randomly chosen from X . Then the probability that P, Q and R form a triangle whose area is a positive integer, is

Two dice are thrown independently Let $A$ be the event that the number appeared on the $1^{\text {st }}$ die is less than the number appeared on the $2^{\text {nd }}$ die, $B$ be the event that the number appeared on the $1^{\text {st }}$ die is even and that on the second die is odd, and $C$ be the event that the number appeared on the $1^{\text {st }}$ die is odd and that on the $2^{\text {nd }}$ is even Then :

A random variable X and its probability distribution is given below. The value of P(X<5) is _______. (rounded off to one decimal place)

X	0	1	2	3	4	5
P(X)	0	K	2K	3K	4K	5K

Given data consists of distinct values of $𝑥_𝑖$ occurring with frequencies $𝑓_𝑖.$ The mean value for the data is _____. (rounded off to one decimal place)

$X_i$	5	6	8	10
$F_i$	8	10	10	12

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event .
Given below are two statements : 
(S1): If $P ( A )=0$, then $A =\emptyset$ 
(S2): If $P(A)=1$, then $A=\Omega$
Then

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are the same. If the probability of a random toss resulting in a head is \(\frac{1}{3}\), then the probability that the experiment stops with the head is

If \(X\sim(5,p)\) \(P(X=3) = 5P(X=4)\), find variance.

If a dice is thrown n-times and probability of getting 7 times odd is equal to 9 times even. Then P(2 even) is \(\frac{K}{215}\) then K is

There are 5 black and 3 white balls in the bag. A die is rolled, we need to pick the number of balls appearing on the die. The probability that the balls are white is?

A bolt manufacturing factory has three products A, B and C. 50% and 30% of the products are A and B type respectively and remaining are C type. Then probability that the product A is defective is 4%, that of B is 3% and that of C is 2%. A product is picked randomly picked and found to be defective, then the probability that it is type C.

In probability distribution for discrete variable x = 0,1, 2 ... P(x = x) = k(x + 1).3–x. The probability of P(x≥2) is equal to?

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is: