Question

Luis Suarez is a soccer player with a barely controllable hunger for human flesh. He 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 B be the the number of games from now until Luis Suarez bites an opponent, and is subsequently suspended. a) Write out the probability mass function for B. b) What is the probability that Luis bites someone in the fourth game from now? c) If Luis 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

According to the question,

B:the number of games from now until Luis Suarez bites an opponent

B takes the values 1,2,3,...

Also, each of the matches Luis plays is independent of the other matches played.

Then, p.m.f. of B is given by--

i.e.

where p= probability that Luis bites an opponent = 0.15

q= probability that Luis does not bite = 1-0.15= 0.85

Then,

(a)

p.m.f. of B is given by--

(b)

Probability that Luis bites someone on the fourth game from now

(c)

Now, as B follows a geometric distribution B will have lack of memory property i.e.

Now,

Probability that he will last more than 10 games without biting an opponent, given Luis promises not to bite anyone in the next 6 games