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Why is a coin flip the perfect example?
A coin flip has only two possible outcomes: Heads or Tails. These are mutually exclusive (can't be both) and exhaustive (must be one of them). This makes them perfect complements!
The Key Insight:
If you didn't get Heads, you must have gotten Tails. There's no third option. So P(Tails) = P(NOT Heads) = 1 - P(Heads).
What makes a coin "fair"?
A fair coin has equal probability of landing Heads or Tails. Neither side is more likely than the other.
Verification (complements must add to 1):
What is a biased coin?
A biased coin doesn't land on Heads and Tails with equal probability. Maybe the coin is weighted, or the flip technique favors one side.
A biased coin has P(Heads) = 0.6 (60%). What is P(Tails)?
We're told the coin is biased toward Heads
60% of the time, this coin lands on Heads.
The remaining probability goes to Tails
Since Heads and Tails are the only options, whatever probability Heads doesn't take, Tails gets.
Result:
The coin lands on Tails 40% of the time.
| Coin Type | P(Heads) | P(Tails) = 1 - P(H) |
|---|---|---|
| Fair coin | 50% | 50% |
| Biased (60% heads) | 60% | 40% |
| Biased (70% heads) | 70% | 30% |
| Biased (25% heads) | 25% | 75% |