Three fair coins tossed together: What is the probability that all three coins show the same face (either all heads or all tails)?
Aptitude
Probability
Difficulty: Easy
Choose an option
-
A1/4
-
B1/3
-
C1/6
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D1/8
Answer
Correct Answer: 1/4
Explanation
Introduction / Context:Tossing three fair coins creates 2^3 equally likely outcomes. We want the probability of the event where all faces match, i.e., either HHH or TTT.
Given Data / Assumptions:
- Coins are fair and independent.
- Sample space size = 8 outcomes.
Concept / Approach:Count favorable outcomes and divide by total outcomes. Favorable = {HHH, TTT} = 2 outcomes.
Step-by-Step Solution:
Total outcomes = 8Favorable outcomes = 2P(all same) = 2/8 = 1/4Verification / Alternative check:Compute P(HHH) + P(TTT) = (1/2)^3 + (1/2)^3 = 1/8 + 1/8 = 1/4.
Why Other Options Are Wrong:1/3 results from averaging; 1/6 confuses with “exactly two heads”; 1/8 counts only one of the two symmetric cases.
Common Pitfalls:Forgetting to include both all-heads and all-tails; mixing up “all same” with “all heads.”
Final Answer:1/4