A collection of field goal kickers are divided into groups 1 and 2. Group i has 3i kickers. On any kick, a kicker from group i will kick a field goal with probability + independent of the outcome of any other kicks.
(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; Kj is the event that kicker j kicks a field goal. Are K1 and K2 independent?
(c) A kicker is selected at random and attempts 10 field goals. Let M be the number of misses. Find P[M = 5].