How to Find Probability of At Least One Head in Coin Flips


For any given coin flip, the probability of getting “heads” is 1/2 or 0.5.

To find the probability of at least one head during a certain number of coin flips, you can use the following formula:

P(At least one head) = 1 – 0.5n

where:

  • n: Total number of flips

For example, suppose we flip a coin 2 times.

The probability of getting at least one head during these 3 flips is:

  • P(At least one head) = 1 – 0.5n
  • P(At least one head) = 1 – 0.53
  • P(At least one head) = 1 – 0.125
  • P(At least one head) = 0.875

This answer makes sense if we list out every possible outcome for 2 coin flips with “T” representing tails and “H” representing heads:

  • TTT
  • TTH
  • THH
  • THT
  • HHH
  • HHT
  • HTH
  • HTT

Notice that at least one head (H) appears in 7 out of 8 possible outcomes, which is equal to 7/8 = 0.875.

Or suppose we flip a coin 5 times.

The probability of getting at least one head during these 5 flips is:

  • P(At least one head) = 1 – 0.5n
  • P(At least one head) = 1 – 0.55
  • P(At least one head) = 1 – 0.25
  • P(At least one head) = 0.96875

The following table shows the probability of getting at least one head during various amounts of coin flips:

probability of at least on head during various coin flips

Notice that the higher number of coin flips, the higher the probability of getting at least one head.

This should make sense considering the fact that we should have a higher probability of eventually seeing a head appear if we keep flipping the coin more times.

Additional Resources

The following tutorials explain how to perform other common calculations related to probabilities:

How to Find the Probability of “At Least One” Success
How to Find the Probability of “At Least Two” Successes
How to Find the Probability of A and B
How to Find the Probability of A or B

One Reply to “How to Find Probability of At Least One Head in Coin Flips”

  1. “For example, suppose we flip a coin **2** times. The probability of getting at least one head during these **3** flips is:”

    Yeah you lost me right there. I guess I don’t understand advanced math.

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