Probability — Important Questions
Madhya Pradesh Board · Class 12 · Mathematics
160 important questions from Probability for Madhya Pradesh Board Class 12 Mathematics, with answers. Written for the board exams 2027.
Interactive on Super Tutor
Studying Probability? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for important questions and more.
Free trial, no card needed.
Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Probability.
Important Questions from Probability
A box contains 4 defective and 6 non-defective items. If 3 items are drawn randomly without replacement, what is the probability that exactly 2 are defective?
Show answer
3/10
P(exactly 2 defective) = C(4,2)×C(6,1)/C(10,3) = (6×6)/120 = 36/120 = 3/10. We choose 2 defective from 4 and 1 non-defective from 6, divided by total ways to choose 3 from 10.
Two events A and B are such that P(A) = 0.4, P(B) = 0.6, and P(A∩B) = 0.24. Are A and B independent events?
Show answer
Yes
For independent events, P(A∩B) = P(A)×P(B). Check: 0.4×0.6 = 0.24, which equals P(A∩B). Since the condition is satisfied, A and B are independent.
A card is drawn from a standard deck of 52 cards. Given that the card is red, what is the probability that it is a heart?
Show answer
1/2
P(Heart|Red) = P(Heart∩Red)/P(Red) = (13/52)/(26/52) = 13/26 = 1/2. Among the 26 red cards, 13 are hearts, so the probability is 13/26 = 1/2.
In a multiple choice test with 4 options per question, what is the probability of getting exactly 2 correct answers out of 3 questions by random guessing?
Show answer
9/64
P(exactly 2 correct) = C(3,2)×(1/4)²×(3/4)¹ = 3×(1/16)×(3/4) = 9/64. Using binomial probability with n=3, k=2, p=1/4.
+156 more questions on Probability (Madhya Pradesh Board Class 12 Mathematics)
Practise AllFrequently Asked Questions
What are the important topics in Probability for Madhya Pradesh Board Class 12 Mathematics?
How many important questions are there in Probability?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Probability
Practice Quiz
Test yourself with a quick quiz
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect
Study Plan
Step-by-step plan for this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
NCERT Solutions
Every textbook question solved step by step
For serious students
Get the full Probability chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Madhya Pradesh Board Class 12 Mathematics. Free to start, no card needed.