Four fair coins are tossed. The probability of either one head or two heads showing up

The probability of getting one head or two heads can be calculated by summing the probabilities of each individual outcome.

The possible outcomes for getting one head are:

- HHHH
- THHH
- HTHH
- HHTH
- HHHT

The possible outcomes for getting two heads are:

- HTHH
- HHTH
- HHHT
- HTTH
- THHH
- TTHH
- HHTT
- HTHT
- THHT
- HTTH

Therefore, there are a total of 15 outcomes that result in either one head or two heads.

Since there are 2^4 = 16 total possible outcomes when flipping four coins, the probability of getting either one head or two heads is 15/16.