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## Suppose you log on to an online chess website and are randomly assigned a match against an opponent. Suppose at any time on the site,

Question

Suppose you log on to an online chess website and are randomly assigned a match against an opponent.

Suppose at any time on the site, 30% of opponents are rated ovice”, 55% are rated mid”, and 15% are

rated high”. In a chess match, a player can either win, lose, or draw. Suppose that you win 75% and

draw 10% of matches against novice rated opponents, you win 50% and draw 20% of matches against

mid rated opponents, and you win 10% and draw 25% of matches against high rated opponents.

(a) For a randomly assigned match, what is the probability that you play someone ranked high and

lose?

(b) For a randomly assigned match, what is the probability that you win?

(c) You play a match and win. What is the probability that you played a high rated opponent?

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Mathematics
6 months
2021-07-17T03:51:21+00:00
2021-07-17T03:51:21+00:00 1 Answers
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## Answers ( )

Answer:a)0.1125 = 11.25% probability that you play someone ranked high and lose.b)0.5435 = 54.35% probability that you winc)0.0690 = 6.90% probability that you played a high rated opponentStep-by-step explanation:Conditional ProbabilityWe use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

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

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 winThis means that

Intersection of events A and B:25% of 15%(high opponent). So

Question:0.0690 = 6.90% probability that you played a high rated opponent