I have a coin which I claim is fair: that is, there is equal chance that it lands on heads and tails, and each flip is independent of every other flip.
But when we look at 60 trials of the coin flipped 5 times (that is, 300 total flips), we see that there are no trials in which either 0 heads were flipped or 5 heads were flipped. Every time, it’s 1 to 4 heads.
This is odd- for a fair coin, there’s a 6.25% chance that we would see 5 tails in a row or 5 heads in a row in a set of 5 flips. To not see that 60 times in a row has a probability of only 2.1%, which is rather unlikely! We can state with some confidence that this coin does not look fair; there is some structure to it that suggests the flips are not independent of each other.
The actual situation is described this way:
I have a coin which I claim is fair: that is, there is equal chance that it lands on heads and tails, and each flip is independent of every other flip.
But when we look at 60 trials of the coin flipped 5 times (that is, 300 total flips), we see that there are no trials in which either 0 heads were flipped or 5 heads were flipped. Every time, it’s 1 to 4 heads.
This is odd- for a fair coin, there’s a 6.25% chance that we would see 5 tails in a row or 5 heads in a row in a set of 5 flips. To not see that 60 times in a row has a probability of only 2.1%, which is rather unlikely! We can state with some confidence that this coin does not look fair; there is some structure to it that suggests the flips are not independent of each other.