Respuesta :
Answer:
a) 0.1125 = 11.25% probability that you play someone ranked high and lose.
b) 0.5435 = 54.35% probability that you win
c) 0.0690 = 6.90% probability that you played a high rated opponent
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
(a) For a randomly assigned match, what is the probability that you play someone ranked high and lose?
15% probability that you play someone that is ranked high.
If you play someone ranked high, 100 - 25 = 75% probability you lose
0.15*0.75 = 0.1125
0.1125 = 11.25% probability that you play someone ranked high and lose.
(b) For a randomly assigned match, what is the probability that you win?
75% of 30%(novice oponent)
50% of 55%(mid oponent)
25% of 15%(high opponent). So
[tex]p = 0.77*0.3 + 0.5*0.55 + 0.25*0.15 = 0.5435[/tex]
0.5435 = 54.35% probability that you win
(c) You play a match and win. What is the probability that you played a high rated opponent?
Here, we use the conditional probability formula.
Event A: Winning
Event B: Playing a high opponent.
0.5435 = 54.35% probability that you win
This means that [tex]P(A) = 0.5435[/tex]
Intersection of events A and B:
25% of 15%(high opponent). So
[tex]P(A \cap B) = 0.25*0.15 = 0.0375[/tex]
Question:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0375}{0.5435} = 0.0690[/tex]
0.0690 = 6.90% probability that you played a high rated opponent
