The chances of exactly one coin being tails are 3 out of 7 (or approximately 42.86%). If the phrase "one
coin being tails" means at least one coin is tails, the chances rise to 6 out of 7 (or approximately 85.71%).
Here is the exact step-by-step breakdown of how this conditional probability works:
1. The Full Possibilities
When you flip three coins, there are 8 possible outcomes in total:
• HHH (3 Heads)
• HHT, HTH, THH (2 Heads, 1 Tail)
• HTT, THT, TTH (1 Head, 2 Tails)
• TTT (3 Tails)
2. Applying the Hint ("At least one is Heads")
Since you are told that at least one coin is heads, you can completely rule out the all-tails scenario (TTT). This shrinks your total pool of possible outcomes from 8 down to 7:
• HHH
• HHT
• HTH
• THH
• HTT
• THT
• TTH
3. Calculating the Final Probability
Depending on how you interpret "one coin being tails," the math changes slightly:
• Interpretation A: Exactly one coin is tails
Looking at our remaining pool of 7 possibilities, there are 3 outcomes that contain exactly one tail: HHT, HTH, and THH.
\(\text{Probability}=\frac{3}{7}\approx 42.86\%\)
• Interpretation B: At least one coin is tails
Looking at our remaining pool of 7 possibilities, every single outcome contains at least one tail except for HHH. That leaves 6 outcomes.
\(\text{Probability}=\frac{6}{7}\approx 85.71\%\)
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