Three fair coins are tossed at the same time. Consider the following statements:
I. The probability that all three coins show heads is \(\frac{1}{6}\).
II. The probability that at least one coin shows a tail is \(\frac{7}{8}\).
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only II
Each coin has 2 equally likely faces, so three coins give \(2^3=\) 8 equally likely outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Statement I — Incorrect.
All heads: HHH only → 1 outcome
Probability \(=\frac{1}{8}\), not \(\frac{1}{6}\)
Statement II — Correct.
At least one tail = every outcome except HHH → \(8-1=7\) outcomes
Probability \(=\frac{7}{8}\)
Only statement II is correct.