Three unbiased coins are tossed simultaneously. What is the probability of getting exactly two heads?
Aptitude
Probability
Difficulty: Easy
Choose an option
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A1/8
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B2/8
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C3/8
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D4/8
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ENone of these
Answer
Correct Answer: 3/8
Explanation
Introduction / Context:Coin-toss probability questions test counting of outcomes under independence. With unbiased coins, each toss has outcomes H or T with equal likelihood, and combined outcomes are equally likely.
Given Data / Assumptions:
- Three independent, fair coins.
- Sample space size = 2^3 = 8 equiprobable outcomes.
- We want exactly two heads.
Concept / Approach:
- Count favorable outcomes using combinations: choose which 2 of the 3 tosses are heads.
- Probability = favorable / total.
Step-by-Step Solution:
Total outcomes = 2^3 = 8Favorable outcomes (exactly two H) = C(3,2) = 3Required probability = 3 / 8Verification / Alternative check:List outcomes: HHT, HTH, THH are the only three with exactly two heads; count = 3 out of 8 total outcomes; probability = 3/8.
Why Other Options Are Wrong:
- 1/8 corresponds to exactly three heads (only HHH).
- 2/8 is not the correct count; it simplifies to 1/4.
- 4/8 (= 1/2) counts “at least two heads,” not “exactly two heads.”
Common Pitfalls:
- Confusing “exactly two” with “at least two.”
- Forgetting outcomes are equally likely only if coins are unbiased.
Final Answer:3/8