Question

3.6.6   A player of a video game is confronted with a series of opponents and has 77% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated.

(a)What is the probability mass function of the number of opponents contested in a game?

(b) What is the probability that a player defeats at least 3 opponents in a game? Round your answer to two decimal places (e.g. 0.98).

(c) What is the expected number of opponents contested in a game? Round your answer to the nearest integer.

(d) What is the probability that a player contests 4 or more opponents in a game? Round your answer to four decimal places (e.g. 0.9876).

(e) What is the expected number of game plays until a player contests 4 or more opponents? Round your answer to the nearest integer.

Answer 1

ANSWER :

A player of a video game is confronted with a series of opponents and has 77% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated.

Given data :

77% probability of defeating each one.

a) The probability mass function of number of opponents contested in a game

P=100-77=23% = 0.23

Def geometric probability :-

The p = 0.77: -

b)

The probability that a player defeats at least 3 opponents in a game :-

Complement rule:

The player defeats two opponents if the player defeated forall game or a later game.

Evaluate the def at k = 1,2,3 :-

c)

The expected number of opponents contested in a game : -

d)

The probability that a player contests 4 or more opponents in a game :-

k = 1,2,3, :-

e)

The expected number of game plays until a player contests 4 or more opponents :-

From part (d)

The expected value is reportal of probability

Expected in 2 game players.