Fifty people are in a line. The first person in the line to have a birthday matching someone in front of them will win a prize. Of course, this means the first person in the line has no chance of winning. Which person has the highest likelihood of winning? Defend your answer with a statistically sound argument.

20th person

Step-by-step explanation:

Before proceeding into problem,assume that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year.

The probability, p(n), of winning a prize when you are the nth person is line is:

(probability that none of the first n−1 people share a birthday)*( probability that you share a birthday with one of the first n−1 people)

So,The first person can't have the same birthday as anyone less by themselves, so lets look at the second person. At the point where we add the second person there is a 364/365 chance of them not sharing a birthday with the previous person. When we add the 3rd person there is there is a 363/365 chance of them not sharing a birthday and so on such that the (n-1)th person when added has a probability of not forming a share of (365 -n -2)/365. We can multiply these together to get the probability that none of first (n-1) people share their birthday.

Therefore the position in line that has highest chance of winning is 20th.