Question

A boxer has, numerous times, bitten an opposing player during a game. If he bites someone again, he will be banned from playing. In any game, the probability he bites an opponent is 0.15. Let the random variable A be the number of games from now until the boxer bites an opponent, and is subsequently suspended.

a) Write out the probability mass function for A.

b) What is the probability that the boxer bites someone in the third game from now?

c) If the boxer promises not to bite anyone in the next six games, what is the probability that he will last more than 10 games without biting an opponent?

Answer 1

The number of games from now until the boxer bites an opponent has geometric distribution with PMF

. Here

a) The PMF is

b) The probability that the boxer bites someone in the third game from now is

c) Define the events,

The probability,

The required conditional probability is