Question

You and two friends each randomly pick a movie from 5 choices. What is the probability that you all pick the same movie?

Answer 1

Solution:
Number of movie choices = 5
Total number of possible ways = Number of ways you can choose a movie from * Number of ways the First friend can choose a movie from * Number of ways the second friend can choose a movie from = 5*5*5 = 125
Now if All pick same movie then
Number of ways you can choose a movie from = 5
Number of ways the first friend can choose a movie from = 1
Number of ways the second friend can choose a movie from = 1
So the total number of all pick the same movie = 5*1*1 = 5
P(That all pick the same movie) = total number of all pick the same movie/Total number of possible ways = 5/125 = 1/25 = 0.04
So there is 4% probability  that you all pick the same movie.