List of top Mathematics Questions on Probability asked in CUET (UG)

In a series of 4 trials, the probability of getting two successes is equal to the probability of getting three successes. The probability of getting at least one success is:

Two events \(X\) and \(Y\) are such that \(P(X) = \frac{1}{3}\), \(P(Y) = n\), and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of \(n\) is:

The probability of a boy winning a game is \( \frac{2}{3} \). Let \( n \) denote the least number of times he must play the game so that the probability of winning the game at least once is more than 90%, and \( X \) denotes that number of times he wins the game. Hence \( n \), mean, variance, and standard deviation of the random variable \( X \) are respectively:
(A) 3
(B) \( \frac{2}{3} \)  
(C) 2  
(D) 0.81  
Choose the correct answer from the options given below: 

A die is thrown three times. Events A and B are defined as below:
A: 6 on the third throw
B: 4 on the first and 5 on the second throw
The probability of A given that B has already occurred, is:

A coin is tossed twice. Then Match List-I with List-II:

List-I	List-II (Adverbs)
(A) P(exactly 2 heads)	(I) \(\frac{1}{4}\)
(B) P(at least 1 head)	(II) \(1\)
(C) P(at most 2 heads)	(III) \(\frac{3}{4}\)
(D) P(exactly 1 head)	(IV) \(\frac{1}{2}\)

Choose the correct answer from the options given below :

If \( P(A) = 0.4 \), \( P(B) = 0.8 \) and \( P(A | B) = 0.6 \), then \( P(A \cup B) \) is:

A pair of dice is rolled . If the two numbers appearing on them are different the probability that
Match List-I with List-II
 

LIST-I(EVENT)	LIST-II(PROBABILITY)
(A) The sum of the number is greater than 11	(i) 0
(B) The sum of the number is 4 or less	(ii) 1/15
(C) The sum of the number is 4	(iii) 2/15
(D) The sum of the number is 4	(iv) 3/15

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Let \( A \) and \( B \) be two independent events such that \( P(A) = \frac{3}{5} \) and \( P(B) = \frac{4}{9} \).

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A coin is tossed K times. If the probability of getting 3 heads is equal to the probability of getting 7 heads, then the probability of getting 8 tails is:

There are 6 cards numbered 1 to 6, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then P(X > 3) is:

Three defective bulbs are mixed with 8 good ones. If three bulbs are drawn one by one with replacement, the probabilities of getting exactly 1 defective, more than 2 defective, no defective, and more than 1 defective respectively are:

The probability of a shooter hitting a target is 3/4 How many minimum number of times must he fire so that the probability of hitting the target at least once is more than 90%?

The probability of not getting 53 Tuesdays in a leap year is:

There are two bags. Bag-1 has 4 white and 6 black balls, and Bag-2 has 5 white and 5 black balls. A die is rolled, and if it shows a multiple of 3, a ball is drawn from Bag-1; otherwise, from Bag-2. If the ball drawn is not black, the probability it was not drawn from Bag-2 is:

Two dice are thrown simultaneously. If $X$ denotes the number of fours, then the expectation of $X$ will be:

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and second throws and a number less than $4$ in the third throw?

A bag contains 6 red, 4 blue and 10 white balls. A ball is picked from the bag at random What is the probability that it is neither white nor blue?

If P(E)=0.05, what is the probability of 'not E'?

Three dice are thrown. The probability of getting a sum of numbers which is a perfect cube, is:

Choose odd one out from the following:

Study the following sequence and then answer the question given below:
9 H 7 Z A 9 2 B C H 3 1 X W V 5 T 4 M 6 0 Q 8 F J.
If every fourth letter/number in the above sequence starting from 7 is eliminated, which of the following will be fifth letter/number to the left of the 12th position from your right?

A pair of dice is thrown and sum of the numbers on two tosses is observed. Which of the statements are correct

Match LIST I with LIST II

List-I		List-II
A	Randomization is used in	I	Unbiased sampling
B	Randomization is not used in.	II	Probability sampling
C	If every element in the population has an equal chance to be part of the selected sample, then the sampling process is called	III	Biased sampling
D	If a sampling process systematically favours certain outcomes over others, then it is called	IV	Non-probability sampling

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A card is drawn at random from a well shuffled pack of 52 cards. What is the probability of getting a ‘two’ of hearts or a ‘three’ of diamonds ?

Two balls are chosen randomly from an urn containing 8 white balls and 4 black balls by a player. Suppose that he wins ₹30 for each black ball selected and loses ₹15 for each white ball selected. The expected value of winning amount is :