At least one head in five flips

Question

You flip a fair coin five times. What is the probability of getting at least one head?

Accepted Answer

Counting all the ways to get at least one head means summing the one-head, two-head, up to five-head cases. Far easier to compute the complement: the single way to get no heads at all. The flips are independent, and each is a tail with probability 	frac12: P(	ext{no heads}) = \left(\frac{1}{2}ight)^5 = \frac{1}{32}. Therefore P(	ext{at least one head}) = 1 - \frac{1}{32} = \frac{31}{32} \approx 0.969. So it is overwhelmingly likely: only about a 3\% chance of whiffing on all five. Takeaway. For "at least one" over independent trials, always compute 1 - P(	ext{none}). The "none" event is…

At least one head in five flips

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