Answer:
0.512 = 51.2% probability that a player defeats at least three opponents in a game
Step-by-step explanation:
Outcomes in which he defeats less than three opponents:
Lose to the first opponent: 0.2 probability.
Beats the first opponent, loses to the second: 0.8*0.2 probability
Beats the first two opponents, loses to the third: 0.8*0.8*0.2 probability:
Probability of losing before beating three opponents:
[tex]P(b < 3) = 0.2 + 0.8*0.2 + 0.8*0.8*0.2 = 0.488[/tex]
What is the probability that a player defeats at least three opponents in a game?
[tex]P(b \geq 3) = 1 - p(b < 3) = 1 - 0.488 = 0.512[/tex]
0.512 = 51.2% probability that a player defeats at least three opponents in a game
