c) Show that P(Ai
) = 1!/4!
d) Show that the probability of at least one match is P (A1
) = 1 - 1/2! + 1/3! - 1/4!
e) Extend this exercise so that there are n balls in the urn. Show that the probability of at least one match is:
) = 1 - 1/2! + 1/3! - 1/4! +...+ (-1)n+1
= 1 - (1- 1/1! + 1/2! - 1/3! +...+ (-1)n
This is exercise 1.4-19 from Probability and Statistical Inference, Hogg and Tanis 8th edition. If anyone could help me with this problem I would greatly appreciate it.