Question

you and 15 other people are asked to think of a number 1-60. if each of you selects a number randomly, what is the probability that at least one of the other people selects the same number that you did?

Answer 1

at least one means not none
that is easier to calculate, then subtract the answer from one

Answer 2

number of ways 15 people can choose from 60 numbers is \(60^{15}\) that is your denominator.
number of way that they are all different from yours: you choose some number. then there are 59 left to choose from. number of ways to do this is \(59^{14}\)

Answer 3

answer is
\[1-\frac{59^{14}}{60^{15}}\]

Answer 4

thanks for the help!

Answer 5

i get about .987 so it is very likely that at least on other person selected your number