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Probability and Statistics Practice Questions

JEE · Mathematics · 1701 free MCQs with instant results and detailed explanations.

1701
Total
399
Easy
778
Medium
524
Hard

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Topics in Probability and Statistics

Mean Variance 422
Conditional Probability 394
Bayes Theorem 452
Random Variables 433

Sample Questions from Probability and Statistics

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

Q1
Easy
A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?
A. 1/2
B. 1/3
C. 1/4
D. 1/6
Show Answer & Explanation
Correct Answer: A
The possible outcomes greater than 2 are {3, 4, 5, 6}. Among these, the even number is 4 and 6, giving us P(Even | >2) = 2/4 = 1/2.
Q2
Easy
If two cards are drawn from a standard deck of 52 cards, what is the probability that the second card is a heart given that the first card drawn was a heart?
A. 12/51
B. 1/4
C. 1/2
D. 13/51
Show Answer & Explanation
Correct Answer: A
After drawing one heart, 12 hearts remain out of a total of 51 cards. Thus, P(Second Heart | First Heart) = 12/51.
Q3
Easy
In a family, there are 3 children. What is the probability that at least one child is a girl given that at least one child is a boy?
A. 3/7
B. 5/7
C. 1/2
D. 2/3
Show Answer & Explanation
Correct Answer: B
Out of the 7 possible combinations of children, 5 have at least one girl. The only combinations with at least one boy are {BBB, BBG, BGB, BGG, GBB, GBG, GGB}.
Q4
Medium
A die is rolled twice. What is the probability of getting at least one '6' given that the sum of the two rolls is greater than 8?
A. 0.5
B. 0.3
C. 0.4
D. 0.6
Show Answer & Explanation
Correct Answer: C
First, we find the outcomes where the sum is greater than 8, then count those that include at least one '6'.
Q5
Medium
A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is red given that it is not blue?
A. 5/5
B. 5/8
C. 5/3
D. 1/2
Show Answer & Explanation
Correct Answer: B
The event that the ball is not blue includes only the red balls, so the probability of drawing a red ball given that it is not blue is 5 red balls out of 8 total balls.
Q6
Medium
If two events A and B are independent, what is the probability of A occurring given that B has occurred?
A. P(A)
B. P(B)
C. P(A) + P(B)
D. 1
Show Answer & Explanation
Correct Answer: A
For independent events, the occurrence of one event does not affect the probability of the other event.
Q7
Medium
A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart given that it is a red card?
A. 1/2
B. 1/4
C. 1/3
D. 2/5
Show Answer & Explanation
Correct Answer: A
There are 26 red cards (13 hearts and 13 diamonds). The probability of drawing a heart from the red cards is 13/26, simplifying to 1/2.
Q8
Hard
Two independent events A and B have probabilities P(A) = 0.4 and P(B) = 0.5. What is the conditional probability P(A|B)?
A. 0.2
B. 0.4
C. 0.5
D. 0.6
Show Answer & Explanation
Correct Answer: B
For independent events, P(A|B) = P(A).
Q9
Hard
A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart given that it is a red card?
A. 0.5
B. 0.25
C. 0.4
D. 0.75
Show Answer & Explanation
Correct Answer: A
Half of the red cards in a deck are hearts.
Q10
Hard
In a bag of 10 balls, 4 are red and 6 are blue. What is the probability of drawing a red ball given that the drawn ball is not blue?
A. 0.4
B. 0.5
C. 0.6
D. 0.3
Show Answer & Explanation
Correct Answer: A
After removing non-blue balls, the remaining are all red, so the probability is 0.4.

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Probability and Statistics — JEE Mathematics Practice Questions Online

This page contains 1701 practice MCQs for the chapter Probability and Statistics in JEE Mathematics. The questions are organized by difficulty — 399 easy, 778 medium, 524 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 4 topics, giving you comprehensive coverage of the entire chapter.