How is the probability of at most one head in several fair coin tosses calculated?

In probability theory, when tossing a fair coin $n$ times, the total number of possible outcomes in the sample space is $2^n$, as each of the $n$ tosses has two possible results (heads or tails).1

To calculate the probability of getting "at most one head," you must account for two mutually exclusive scenarios:

• Zero heads: There is only one outcome where no heads occur (all tails).1
• Exactly one head: There are $n$ possible outcomes where exactly one head occurs, as the head can appear on the first, second, ..., or $n$th toss.1

By the principle of additivity, the total number of favorable outcomes is the sum of these cases, which is $n+1$. Therefore, the probability of obtaining at most one head is:

$$\frac{n+1}{2^n}$$

This calculation assumes that all outcomes in the sample space are equally likely.1