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If I toss a biased coin $n$ times, what is the probability of getting at least $i$ heads?

The probability of getting exactly $i$ heads with an unbiased coin is $\binom{n}{i}2^{-n}$ I think.

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2 Answers 2

up vote 4 down vote accepted

The probability is represented by a binomial distribution. Let $K$ be the number of heads. Say the probability of getting a head is $p$. Then to get at least $i$ heads out of $n$ flips is

$$P(K \ge i) = \sum_{j=i}^n \binom{n}{j} p^j (1-p)^{n-j}$$

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Let $H$ be the number of heads you get.

$$P(H \geq i) = P(H = i) + P(H = i+1) + P(H = i+2) + \cdots $$

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