What is the probability that when a fair coin is flipped 25 times, there will be exactly five heads?

Use the Binomial Probability rule, letting X = 5. This denotes the number of heads we want.



This means that in 25 spaces, we want exactly 5 of these spaces to be heads, leaving the other 20 to be tails (25C5). Now, we just need to find the probability of each event occurring. Since it's a fair coin, there is a 1/2 chance at getting a head, and 1/2 chance at getting a tail.

Since we want 5 heads, we want this event to occur 5 times:


and vice-versa for tails.
Thus, we get the answer above.

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