The probability of flipping at least one head in two coin flips is 3/4, or 75%. This is calculated by adding the probabilities of flipping one head (1/2) and two heads (1/4) together, which gives 3/4. The probability of flipping at least one head in three coin flips is 7/8, or 87.5%. This is calculated by adding the probabilities of flipping one head (1/2), two heads (1/4), and three heads (1/8) together, which gives 7/8.
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.
The following tutorials explain how to perform other common calculations related to probabilities: