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:

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