for this question i am confuse why the function need times 2

for this question, i am confuse why the function need times 2. thank you

Odd Person out Recall Example 6 from September 21st. As a reminder, this games involves N people, and works like this: Suppose a coffee truck pulls into a company parking lot. N people greet the truck, each of which wish to have a cup of coffee. In \"odd person out\", each of N people independently toss a presumed to be fair coin at the same time. If all the coins but one shows the same face, then the odd person out is the one who pays for coffee (for all N people!). Otherwise, all N people flip the coin again. On average, how many flips are required to get an odd person out when N people are vying for coffee? Define the random variable X as the number of times the N flips of a coins needs to happen in order to have the odd person out. Clearly, X = 1,2,3,.., We derived the probability distribution function that allows us to find the probability of observing an \'odd person out\' on any turn as: P = (N N - 1) (1/2)^N-1 (1/2) 2 = 2N(1/2)^N = N / 2N - 1

Solution

because it can be 2 options, I mean the probability can happen 2 times for the problem that you are solving