Question

1.3-9. An urn contains four balls numbered 1 through 4 The balls are selected one at a time without replacement. A match occurs if the ball numbered m is the mth ball selected. Let the event A, denote a match on the ith draw i 1,2, 3, 4. 3! (a) Show that P(A)for each i 4! 2! (b) Show that P(A, nA,) =-, i 1! (d) Show that the probability of at least one match is (e) Extend this exercise so that there are n balls in the urn. Show that the probability of at least one match is P(A1 U A2 U.UAn) ( What is the limit of this probability as n increases without bound?

Answer 1

e no, 3 I n! (LI)+ I n+ I! 21 3! nl 2! 3! ngennerd 31 y1 ve than note: !! 21 31-41 2! 3! n we ndle: etureaAg)드 1-(1.lt I -l t )elee el.e. 1! 21 lhank s