We want to see the probability of 3 or more people sharing the same birthday in a room with a random sample of 23 people
k = 23 # number of people in room
p <- numeric(k) # create numeric vector to store probabilities
for (i in 1:k) {
q <- 1 - (0:(i - 2))/365 # 1 - prob(no matches)
p[i] <- 1 - prod(q) }
prob <- p[k]
prob
## [1] 0.4756953
plot(p, main="Probability at least 3 people have same Birthday", xlab ="Number of People", ylab = "Probability", col="blue")