Question

A pinball machine has 7 holes through which a ball can drop. Five balls are played and we observe which hole each ball goes down. For example, the first ball could go down hole 1, hole 2, ..., or hole 7 (similarly for the other 4 balls). On each play, assume the ball is equally likely to go down any one of the 7 holes. Find the probability that more than one ball goes down at least one of the holes.

Answer 1

Total sample space = 7⁵ = 16807

Sample outcome for no ball goes down the same hole again = 7 * 6 * 5 *4 * 3 = 2520

P(more than one ball goes down at least one of the holes) = 1 - P(no ball goes down the same hole again)

                                                                                             = 1 - 2520/16807

                                                                                             = 0.85 (ans)