There is a collection of field goal kickers, which can be divided into two groups 1 and 2. Group i has 3i kickers. On any kick, a kicker from group i will kick a field goal with probability 1/(i + 1), independent of the outcome of any other kicks by that kicker or any other kicker.
(a) A kicker is selected at random from among all the kickers and attempts one field goal. Let K be the event that a field goal is kicked. Find P[K].
(b) Two kickers are selected at random. For j = 1, 2, let K j be the event that kicker j kicks a field goal. Find P[K1 ∩ K2]. Are K1 and K2 independent events?
(c) A kicker is selected at random and attempts 10 field goals. Let M be the number of misses. Find P[M = 5].