You flip a coin n times and keep a record of the results. In how many ways could you obtain at least one tail?

Answer 1

When you flip a two-sided coin n times, there are 2^n possible outcomes.

For example, flip 3 times, have results of 0-7, or 8 possible outcomes.

Only one of those outcomes had "no tails," (let's say that all 0 represent all heads) which means that all of the others have "at least one tail."

So, for n flips of a two-sided coin, the "number of ways that you could obtain at least one tail" is:

2^n - 1



Answer 2

At least one tail means not all heads, therefore use the compliment,

1 - (1/n!)