Probability Distributions — Practice Quiz
Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce
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Quick Quiz: Probability Distributions
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A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?
A die is thrown 4 times. If getting an even number is success, what is the probability of exactly 2 successes?
If X ~ B(n, p) and E(X) = 6, Var(X) = 4.2, then n = ?
In 8 tosses of a fair coin, what is the probability of getting at least 6 heads?
Sample Questions
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.
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.
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.
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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