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Important Questions

Probability

Madhya Pradesh Board · Class 12 · Mathematics

Most important questions from Probability for Madhya Pradesh Board Class 12 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

160 questions50 flashcards5 concepts

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A Venn diagram illustrating a partition of a sample space S into several pairwise disjoint and exhaustive events E1, E2, ..., En.
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160 Questions·
multiple choicemultiple correctshort answernumericaltrue false

Sample Questions

1multiple choice

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?

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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.

2multiple choice

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?

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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.

3multiple choice

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?

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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.

4multiple choice

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?

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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.

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Frequently Asked Questions

What are the important topics in Probability for Madhya Pradesh Board Class 12 Mathematics?
Probability covers several key topics that are frequently asked in Madhya Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Probability — Madhya Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 160 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Probability?
There are 160 practice questions available for Probability. These cover multiple question types including MCQs, short answer, and long answer questions.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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