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?

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

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 win

This 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

answer: 819.89 miles across america

step-by-step explanation:

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation: