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Important Questions

Probability

Himachal Pradesh Board · Class 12 · Mathematics

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

48 questions25 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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48 Questions·
multiple choicemultiple correctshort answerlong answer

Sample Questions

1multiple correct

Two coins are tossed simultaneously. Which of the following events are independent?

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First coin shows head and second coin shows head, First coin shows head and second coin shows tail

Independent events are those where the occurrence of one doesn't affect the other. The result of the first coin doesn't influence the second coin, so options 1 and 2 are correct. Options 3 and 4 involve dependencies between the events.

2multiple 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.

3multiple 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.

4multiple 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.

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Frequently Asked Questions

What are the important topics in Probability for Himachal Pradesh Board Class 12 Mathematics?
Probability covers several key topics that are frequently asked in Himachal 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 — Himachal Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 48 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 48 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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