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Probability with combinations (coins and choices)
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Learn it When n coins are tossed there are $2^n$ equally likely outcomes. The number with exactly k heads is $\binom{n}{k}$, so P(exactly k heads) $= \frac{\binom{n}{k}}{2^n}$.
Example: 6 coins are tossed. P(exactly 3 heads)?
- Total outcomes: $2^6 = 64$.
- Ways to choose which 3 coins are heads: $\binom{6}{3} = 20$.
- P $= \frac{20}{64} = \frac{5}{16}$.
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