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Probability Practice Questions

JEE · Mathematics · 1887 free MCQs with instant results and detailed explanations.

1887
Total
419
Easy
864
Medium
604
Hard

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Topics in Probability

Bayes' Theorem 355
Random Variables 275
Mean and Variance 262
Binomial Distribution 309
Conditional Probability 322
Classical Probability 364

Sample Questions from Probability

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
If a die is rolled, what is the probability of getting an even number?
A. 1/2
B. 1/3
C. 1/4
D. 1/6
Show Answer & Explanation
Correct Answer: A
The even numbers on a die are 2, 4, and 6. There are 3 even numbers out of 6 possible outcomes.
Q2
Easy
If you flip a fair coin three times, what is the probability of getting exactly two heads?
A. 3/8
B. 1/2
C. 1/4
D. 1/8
Show Answer & Explanation
Correct Answer: A
The total outcomes for 3 flips is 2^3 = 8. The favorable outcomes for exactly 2 heads are: HHT, HTH, THH (3 ways). Thus, the probability is 3/8.
Q3
Easy
In a lottery, the winning numbers are 123, 456, and 789. What is the probability of selecting a winning number if you choose one number?
A. 1/100
B. 1/30
C. 1/3
D. 3/100
Show Answer & Explanation
Correct Answer: B
There are 3 winning numbers and assuming a total of 30 possible numbers, the probability is 3 winning / 30 total = 1/10.
Q4
Medium
In a class of 40 students, 25 students play cricket, 15 play football, and 10 play both. What is the probability that a randomly selected student plays at least one of the two games?
A. 0.5
B. 0.75
C. 0.65
D. 0.4
Show Answer & Explanation
Correct Answer: B
Using the principle of inclusion-exclusion, the number of students playing at least one game = 25 + 15 - 10 = 30. Probability = 30/40 = 0.75.
Q5
Medium
In a lottery, there are 100 tickets and 10 winning tickets. What is the probability of picking a winning ticket?
A. 1/10
B. 1/20
C. 1/100
D. 1/5
Show Answer & Explanation
Correct Answer: A
The probability of picking a winning ticket is the ratio of winning tickets to total tickets, which is 10/100 = 1/10.
Q6
Medium
A bag contains 4 red balls and 6 blue balls. If one ball is drawn at random, what is the probability that it is red?
A. 0.4
B. 0.6
C. 0.5
D. 0.3
Show Answer & Explanation
Correct Answer: A
The probability of drawing a red ball is the number of red balls divided by the total number of balls. Here, it is 4/(4+6) = 0.4.
Q7
Medium
Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the two dice is 7?
A. 1/6
B. 1/12
C. 5/36
D. 1/36
Show Answer & Explanation
Correct Answer: A
There are 6 combinations that give a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). The total combinations when two dice are thrown are 36. Hence, the probability is 6/36 = 1/6.
Q8
Hard
A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random, what is the probability that both are red?
A. 1/6
B. 1/10
C. 2/9
D. 1/20
Show Answer & Explanation
Correct Answer: B
The total ways to select 2 balls from 10 is C(10,2) = 45. The ways to select 2 red balls from 5 is C(5,2) = 10. Thus, the probability is 10/45 = 1/4.5 = 1/10.
Q9
Hard
Two dice are rolled. What is the probability of getting a sum of 8?
A. 5/36
B. 1/12
C. 1/6
D. 7/36
Show Answer & Explanation
Correct Answer: A
The favorable outcomes for a sum of 8 are (2,6), (3,5), (4,4), (5,3), (6,2). That's 5 outcomes out of 36 possibilities.
Q10
Hard
In a class of 30 students, 18 students like Mathematics, 15 like Physics, and 10 like both. What is the probability that a student chosen at random likes either Mathematics or Physics?
A. 0.67
B. 0.50
C. 0.83
D. 0.75
Show Answer & Explanation
Correct Answer: C
Using the principle of inclusion-exclusion: P(M ∪ P) = P(M) + P(P) - P(M ∩ P) = (18/30) + (15/30) - (10/30) = 23/30.

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More Mathematics Chapters

1 Sets Relations and Functions
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2 Complex Numbers
1613 Qs →
3 Matrices and Determinants
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4 Permutations and Combinations
1645 Qs →
5 Limits Continuity and Differentiability
1661 Qs →
6 Integral Calculus
1623 Qs →
7 Differential Equations
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8 Coordinate Geometry
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Probability — JEE Mathematics Practice Questions Online

This page contains 1887 practice MCQs for the chapter Probability in JEE Mathematics. The questions are organized by difficulty — 419 easy, 864 medium, 604 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 6 topics, giving you comprehensive coverage of the entire chapter.