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

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )