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Probability Distributions

Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce

Practice quiz for Probability Distributions — Maharashtra Board Class 12 Mathematics & Statistics -Commerce. MCQs and questions with answers to test your preparation.

45 questions20 flashcards4 concepts

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Quick Quiz: Probability Distributions

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1

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

2

A die is thrown 4 times. If getting an even number is success, what is the probability of exactly 2 successes?

3

If X ~ B(n, p) and E(X) = 6, Var(X) = 4.2, then n = ?

4

In 8 tosses of a fair coin, what is the probability of getting at least 6 heads?

45 Questions·
multiple choicemultiple correct

Sample Questions

1multiple correct

Which of the following are requirements for Bernoulli trials?

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Each trial has exactly two outcomes, Probability of success remains constant, Trials must be independent

Bernoulli trials require: (1) Exactly two outcomes (success/failure), (2) Constant probability of success in each trial, and (3) Independence of trials. The number of trials can be any finite number.

2multiple correct

Which of these situations represent Bernoulli trials?

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Drawing cards with replacement, Tossing a coin multiple times, Rolling a die and noting if result is 6

Bernoulli trials require constant probability and independence. Drawing with replacement, coin tosses, and die rolls maintain constant probability. Without replacement changes probabilities between trials.

3multiple choice

A bag contains 4 red and 6 black balls. If 3 balls are drawn with replacement, what is the probability of getting exactly 2 red balls?

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12/125

P(red) = 4/10 = 2/5, P(black) = 6/10 = 3/5. P(X=2) = ³C₂ × (2/5)² × (3/5)¹ = 3 × 4/25 × 3/5 = 36/125 = 12/125. Wait, let me recalculate: 3 × 4/25 × 3/5 = 36/125. This doesn't match the answer. Let me recalculate: 3 × (4/25) × (3/5) = 3 × 12/125 = 36/125. The calculation shows 36/125, but the given answer is 12/125. Let me check: ³C₂ × (2/5)² × (3/5) = 3 × (4/25) × (3/5) = 36/125. There seems to be an error in the provided answer.

4multiple choice

If X ~ B(10, 0.3), then E(X) = ?

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3

For binomial distribution, E(X) = np. Here n = 10, p = 0.3. Therefore, E(X) = 10 × 0.3 = 3

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Frequently Asked Questions

What are the important topics in Probability Distributions for Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Probability Distributions covers several key topics that are frequently asked in Maharashtra 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 Distributions — Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

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

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