Three fair coins tossed together: What is the probability that all three coins show the same face (either all heads or all tails)?

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:

Verification / 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