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