List of top Mathematics Questions on Probability asked in BITSAT

A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
A box contains 5 red balls and 4 green balls. Two balls are drawn one after another without replacement. What is the probability that the second ball is green, given that the first ball drawn was red?
Two numbers are selected at random (without replacement) from the first 6 natural numbers. What is the probability that the difference of the numbers is less than 3?
Two dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is at least 10?
From a group of 10 men and 8 women, a committee of 5 is to be formed such that it contains at least 3 women. How many such committees are possible?
A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9, is
Given below is the distribution of a random variable \(X\):
\[ \begin{array}{|c|c|} \hline X = x & P(X = x) \\ \hline 1 & \lambda \\ 2 & 2\lambda \\ 3 & 3\lambda \\ \hline \end{array} \] If \(\alpha = P(X<3)\) and \(\beta = P(X>2)\), then \(\alpha : \beta = \)
The probability that certain electronic component fails when first used is 0.10. If it does not fail immediately, the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is
The probability of getting 10 in a single throw of three fair dice is:
The probability of getting a sum greater than 7 when a pair of dice are thrown is:
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
If \( P(B) = \frac{3}{5} \), \( P(A \mid B) = \frac{1}{2} \), and \( P(A \cup B) = \frac{4}{5} \), then the value of \( P(A \cup B)' + P(A' \cup B) \) is:
Bag P contains 6 red and 4 blue balls, and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
A pack of cards contains 4 aces, 4 kings,4 queens, 4 jacks. Two cards are drawn from the deck, find out the probability that at least one of them is ace.
What is the probability of 53 Fridays in an ordinary year?
A random variable X has the probability distribution
X: 1, 2, 3, 4, 5, 6, 7, 8
P(X): 0.15, 0.23, 0.12, 0.10, 0.20, 0.08, 0.07, 0.05
For the events E = X is a prime and F = X < 4, find P(E ∪ F).
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
One mapping is selected at random from all mappings of the set S=1,2,3,…,n into itself. The probability that it is one–one is (3)/(32). Then the value of n is
If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is
A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is
A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is
A bag contains (2n+1) coins. It is known that n of these coins have a head on both sides, whereas the remaining (n+1) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is (31)/(42), then n is equal to
A bag contains $2n$ coins out of which $n-1$ are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is $\frac{41}{56}$, then the number of unfair coins in the bag is
The probability of getting 10 in a single throw of three fair dice is: