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Probability Questions

Practice 81 Probability questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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81
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1
Easy
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75
Medium
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5
Hard
Practice by Exam:Mathematics(74)Quantitative Aptitude(4)Reasoning Ability(2)General Aptitude(1)

About Probability — practice questions, PYQs & concepts

Probability is a frequently-tested topic on Mathematics, Quantitative Aptitude, Reasoning Ability. ExamTest.live currently lists 81 Probability questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Probability weight in competitive exams

Across our Probability question bank, the largest sources are Mathematics (74), Quantitative Aptitude (4), Reasoning Ability (2) and General Aptitude (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 1 easy Probability questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Probability Questions(1–81 of 81)

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Q1mediummcqMathematicsMathematics Mock Test - 62026
9% accuracy
In a box containing eggs, eggs are rotten. The probability that out of a sample of eggs none is rotten (if sampling is with replacement) is:
Q2mediummcqMathematicsMathematics Mock Test - 62026
13% accuracy
Let and be two mutually exclusive events. Let denote the probability. Which of the following statements is true?
Q3mediummcqMathematicsMathematics Mock Test - 62026
9% accuracy
The value of for which can serve as the probability function of a random variable that takes values is:
Q4mediummcqMathematicsMathematics Mock Test - 62026
9% accuracy
The probability density function for a continuous random variable is: The mean value of is:
Q5mediummcqMathematicsMathematics Mock Test - 62026
9% accuracy
Two events and are independent and equally likely. If , then ?
Q6mediummcqMathematicsMathematics Mock Test - 102026
18% accuracy
Below is a figure indicating a sample space and the probability of occurrences of events and . Which colored section of the portion will indicate the probability of events and occurring simultaneously?
Q7mediummcqMathematicsMathematics Mock Test - 12026
0% accuracy
If , , and , then is equal to:
Q8mediummcqMathematicsMathematics Mock Test - 12026
9% accuracy
The chances of a defective screw in three boxes A, B, and C are , , and respectively. A box is selected at random and a screw is found to be defective. Find the probability that it came from box A.
Q9mediummcqMathematicsMathematics Mock Test - 12026
9% accuracy
If four dice are thrown together, what is the probability that the sum of the numbers appearing on them is 25?
Q10mediummcqMathematicsMathematics Mock Test - 12026
18% accuracy
Suppose , , and . If and are independent events, then the value of is:
Q11mediummcqMathematicsMathematics Mock Test - 102026
18% accuracy
and are two independent witnesses in a case. The probability that will speak the truth is and the probability that will speak the truth is . If and agree on a certain statement, then the probability that the statement is true is:
Q12mediummcqMathematicsMathematics Mock Test - 102026
9% accuracy
For any two events and , and . Then which of the following is NOT correct?
Q13mediummcqMathematicsMathematics Mock Test - 102026
27% accuracy
A fair die is thrown six times. The probability of getting a factor of 6 exactly four times is:
Q14mediummcqMathematicsMathematics Mock Test - 102026
9% accuracy
A continuous random variable has the probability density function: is equal to:
Q15mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
In throwing a six-faced die, let A be the event that an even number occurs, B be the event that an odd number occurs, and C be the event that a number greater than 3 occurs. Which one of the following is correct?
Q16mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Let for . The value of constant such that satisfies the conditions of being a probability mass function (PMF) is:
Q17mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
A fair die is tossed thrice. If the probabilities of zero, one, two, and three successes are respectively, find the mean of the number of successes.
Q18mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Given , , and . Find .
Q19mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
In the following table, is the discrete random variable and is the probability density function. The standard deviation of is:| | | | | ||---|---|---|---|---|| | | | | |
Q20mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
What is the probability of getting a numbered card when a card is drawn from a 52-card pack?
Q21mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
The mean of the probability distribution function given by the following table will be:\begin{center}\begin{tabular}{|c|c|c|c|c|c|}\hline & 1 & 2 & 3 & 4 & 5 \ \hline & 0.2 & 0.35 & 0.25 & 0.15 & 0.05 \ \hline\end{tabular}\end{center}
Q22mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
A coin is tossed twice. If and denote the occurrence of a head on the first toss and second toss respectively, then what is equal to?
Q23mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
Given that is a random variable in the range with a probability density function , the value of the constant is:
Q24mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
is a random variable with probability density function:

Then is:
Q25mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
For a continuous random variable distributed in the interval , the probability is:
Q26mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Let be a discrete random variable with probability for . Then the expected value of is:
Q27mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
What is the probability that the roots of the equation are real, where and ?
Q28mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
Let be a random variable that is uniformly chosen from the set of positive odd numbers less than . The expectation is:
Q29mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
If the expected value of a random variable is 2 and its variance is 1, then what will be the variance of ?
Q30mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
Five coins are tossed at a time. The probability of obtaining at least one head is:
Q31mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Consider the probability distribution function defined as . Which of the following is true?
Q32mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
A coin is tossed times. The probability of head is . The probability of exactly heads is:
Q33mediummcqQuantitative AptitudeMock Test2026
0% accuracy
A basket has apples, mangoes, and oranges. One fruit is selected at random. What is the probability that it is neither an apple nor a mango?
Q34mediummcqQuantitative AptitudeMock Test2026
0% accuracy
A box contains identical red balls and identical blue balls. How many distinct ways can these balls be arranged in a row?
Q35hardmcqMathematicsAIEEE 20042026
0% accuracy
The probability that speaks truth is while this probability for is The probability that they contradict each other when asked to speak on a fact is
Q36hardmcqMathematicsAIEEE 20042026
0% accuracy
A random variable has the probability distribution:
image
For the events and the probability is
Q37hardmcqMathematicsAIEEE 20042026
0% accuracy
The mean and the variance of a binomial distribution are and respectively. Then the probability of successes is
Q38mediummcqMathematicsAIEEE 20062026
0% accuracy
At a telephone enquiry system, the number of phone calls regarding relevant enquiry follows a Poisson distribution with an average of phone calls during time intervals. The probability that there is at most one phone call during a time period is:
Q39mediummcqMathematicsAIEEE 20072026
0% accuracy
A pair of fair dice is thrown independently three times. The probability of getting a score of exactly twice is:
Q40mediummcqMathematicsAIEEE 20072026
0% accuracy
Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are and , respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is:
Q41mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
In a job placement event, there are aspirants attending a company interview, out of which are females. It is known that of the females are graduates. Determine the probability that an aspirant selected randomly is a graduate given that the selected aspirant is a female?
Q42mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If and are random variables such that , and , , the values of such that will be:
Q43mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Which of the following is true for binomial distribution?
Q44mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Urn A consists of blue and green balls while another urn B consists of blue and green balls. One ball is drawn at random from one of the urns and it is found to be blue. Determine the probability that it was drawn from urn B?
Q45mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Find the number of ways of picking cards from a set of playing cards if all four cards are of the same suit?
Q46mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
The variance of a random variable is given by:
Q47mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
A card is drawn at random from a pack of cards. What is the probability that the card drawn is either an Ace or a King?
Q48mediummcqMathematicsMathematics Mock Test - 82026
A family has two children. If the first child is a boy, find the probability that the other child is also a boy.
Q49mediummcqQuantitative AptitudePractice Paper2026
A student randomly picks a day from the days of a week. What is the probability that the selected day starts with the letter 'W' or 'S' ?
Q50mediummcqMathematicsMathematics Mock Test - 112026
If the probability of to fail in an examination is and that for is , then the probability that either or fails (meaning exactly one of them fails) is:
Q51mediummcqMathematicsMathematics Mock Test - 112026
A coin is tossed times. If is a random variable representing the number of tails, then the mathematical expectation of is:
Q52mediummcqQuantitative AptitudeCompetitive Exam2026
A committee of members is to be formed from men and . What is the probability that the committee contains at least one woman?
Q53mediummcqReasoning AbilityPractice Test2026
There are different symbols. A code is formed by selecting symbols such that each symbol can be used only once (that is, no symbol is repeated in the code). Also, the order of symbols matters. How many different codes can be formed?
Q54mediummcqReasoning AbilityPractice Test2026
A coin is flipped two times. What is the probability of getting at least one head?
Q55mediummcqMathematicsMathematics Mock Test - 82026
If an event has only one sample point of a sample space, it is called a ______:
Q56mediummcqMathematicsAIEEE2026
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is:
Q57mediummcqMathematicsAIEEE2026
A random variable has Poisson distribution with mean . Then equals:
Q58mediummcqMathematicsAIEEE2026
Let and be two events such that , and , where stands for complement of event . Then events and are:
Q59mediummcqMathematicsAIEEE-CBSE-ENG-032026
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is:
Q60mediummcqMathematicsAIEEE-CBSE-ENG-032026
Events are mutually exclusive events such that , and . The set of possible values of are in the interval:
Q61mediummcqMathematicsAIEEE-CBSE-ENG-032026
The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then is:
Q62mediummcqMathematicsAIEEE2026
It is given that the events and are such that , and . Then is:
Q63mediummcqMathematicsAIEEE2026
A die is thrown. Let be the event that the number obtained is greater than . Let be the event that the number obtained is less than . Then is:
Q64mediummcqMathematicsAIEEE 20092026
In a binomial distribution , if the probability of at least one success is greater than or equal to , then is greater than:
Q65mediummcqMathematicsAIEEE 20092026
One ticket is selected at random from tickets numbered . Then the probability that the sum of the digits on the selected ticket is , given that the product of these digits is zero, equals:
Q66hardmcqMathematicsAIEEE2026
Four numbers are chosen at random (without replacement) from the set .Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is .Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is .
Q67mediummcqMathematicsAIEEE2026
There are two urns. Urn has distinct red balls and urn has distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is:
Q68easymcqMathematicsAIEEE2026
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is:
Q69hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
Consider independent Bernoulli's trials each with probability of success . If the probability of at least one failure is greater than or equal to , then lies in the interval:
Q70mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If and are two events such that and , then the correct statement among the following is:
Q71mediummcqMathematicsAIEEE 20122026
Three numbers are chosen at random without replacement from . The probability that their minimum is 3, given that their maximum is 6, is:
Q72mediummcqMathematicsJEE Main2026
A multiple choice examination has questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get or more correct answers just by guessing is:
Q73mediummcqMathematicsMathematics Mock Test - 32026
The mean of the numbers obtained on throwing a die having written on four faces, on three faces, on two faces and on one face is?
Q74mediummcqMathematicsMathematics Mock Test - 32026
A pair of fair dice is thrown. What is the probability of getting a six on both, given at least one die gets six?
Q75mediummcqMathematicsMathematics Mock Test - 32026
Let and be two events such that , and . Then, events and are:
Q76mediummcqMathematicsMathematics Mock Test - 32026
A continuous random variable has uncountably many values in the interval . If is a value in the interval , then is:
Q77mediummcqMathematicsMathematics Mock Test - 82026
Let and be two independent Binomial random variables such that and . If , find (i) and (ii) .
Q78mediummcqMathematicsMathematics Mock Test - 82026
A die is thrown 3 times. Let Event A be "4 on the 3rd throw" and Event B be "6 on the 1st and 5 on the 2nd throw". What is the probability of A given that B has already occurred?
Q79mediummcqMathematicsMathematics Mock Test - 82026
A player tosses three coins. If the first toss is a Head, find the probability that there are two consecutive Heads among the three coins.
Q80mediummcqMathematicsAIEEE 20042004
0% accuracy
The number of ways of distributing identical balls in distinct boxes so that none of the boxes is empty is
Q81mediummcqGeneral AptitudeGeneral Aptitude
8% accuracy
A fair six-faced dice, with the faces labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, is rolled thrice. What is the probability of rolling ‘6’ exactly once?

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Which exams include Probability questions?▼
Probability questions are commonly asked in Mathematics, Quantitative Aptitude, Reasoning Ability, General Aptitude. You can filter by exam using the links above.
How do I practice Probability questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.