Tran flips a coin 4 times. what results are the lowest probabilities of happening

That's a very interesting question.

Here's the way I thought about it, and the answer I came up with

while avoiding the need to define and count every possible outcome:

- - There are (2 x 2 x 2 x 2) = 16 possible outcomes of 4 flips.

- - There are several different ways to get 1 heads and 3 tails.

- - There are several different ways to get 2 heads and 2 tails.

- - There are several different ways to get 3 heads and 1 tails.

- - But there's only one way to get heads all 4 times,

and there's only one way to get tails all 4 times.

- - So there are 2 ways for all 4 flips to produce the same face.

The probability of that is 2/16 = 1/8 = 12.5%, and I'm saying

that this is the least probable result of 4 flips.