Question

What is the probability that at least 2 of the presidents of the United States have died on the same day of the year? If you bet this has happened, would you win your bet?

Christian’s Response

To solve the problem, we first have to solve for the probability the each president will have died on unique days of the year. Lastly, we subtract 1 from the result in order to get the inverse of this statement. By subtracting by 1, we get the opposite of the statement - which gives us the probability atleast 2 presidents have died on the same day of the year.

# total number of presidents
n <- 46 

# multiplies in sequence the probability that each president passes on a unique day
prob_all_not <- prod((365:(365-n+1))/365) 
atleast_2 <- 1 - prob_all_not 

atleast_2
## [1] 0.9482528

In this scenario, there is around a 95% probability that atleast 2 presidents will have passed on the same day. If we were to make a bet, there would be a high chance of correctly predicting this event to take place.