Hi,
I have got following question from a book:

Consider football game between two riual teams: Team0 and Team1 . Suppose Team 0 wins 65% of the time and Team 1 wins the remaining
matches. Among the games won by Team 0, only 30% of them come from playing on Team1 's football field. On the other hand,75% of the
victories for Team1 are obtained while playing at home. If Team 1 is to host the next match between the two teams, which team will most likely
emerge as the winner?

Book provided the solution also but I cant understand:

Book says that:

let X be the
random variable that represents the team hosting the match and Y be the
random variable that represents the winner of the match.

Mine:
X is hosting the match, therefore X=1 (Is this correct?)

Again book says: Both X & Y can take on the values {0, 1} from the set.

I cant understand what this {0, 1} mean? Is it the team # as mentioned in the question or is it the probability?

Some body please guide me.

Zulfi.

 

To answer the question, just ask what the variables whose values can take on {0, 1} represent.

X is THE TEAM hosting the match, and Y is the WINNER of the match.

So if X = 0, does it make more sense to say that the team hosting the match is Team 0, or that the team hosting the match is probability 0?

Similarly, if Y = 1, does it make more sense to say that the winner of the match is Team 1, or that the winner of the match is probability 1?

 

To answer the question, just ask what the variables whose values can take on {0, 1} represent.

X is THE TEAM hosting the match, and Y is the WINNER of the match.

So if X = 0, does it make more sense to say that the team hosting the match is Team 0, or that the team hosting the match is probability 0?

Similarly, if Y = 1, does it make more sense to say that the winner of the match is Team 1, or that the winner of the match is probability 1?

Thanks you are right. I got it.
X is the team hosting the match and X has a probability 0 (also because X has won 35% of matches.)
Y is the winner of the match so Y has a probability 1 (also because Y has won 65% of matches)
Is the above correct? (specially the thing after because).

Zulfi.

 

Thanks you are right. I got it.
X is the team hosting the match and X has a probability 0 (also because X has won 35% of matches.)
Y is the winner of the match so Y has a probability 1 (also because Y has won 65% of matches)
Is the above correct? (specially the thing after because).

Zulfi.

What you are saying makes no sense.

X is the team that is hosting the match. If X=0, then Team 0 is hosting the match. If X=1, then Team 1 is hosting the match. That's ALL that X tells you. There is no probability involved.

Y is the team that won the match. If Y=0, then Team 0 won the match. If Y=1, then Team 1 won the match. That's ALL that Y tells you. There is no probability involved.

You are basically being asked to find which of the following is greater:
The probability that Y=0 given that X=1, or the probability that Y=1 given that X=1.

Think of an extreme case with hard numbers.

Team 0 and Team 1 have played 1000 games and Team 0 has won 900 of them.

When the two teams play next, knowing only this information, which team is more likely to win?

Now, what if I give you some additional information and that is that each team has lost every game that it hosted (and won every game that it played at the other team's field).

Now I tell you that Team 0, which has won 90% of the games, is hosting the next game. Who do you think is more likely to win now?

 

Hi,
Thanks for your help. It greatly helped me. I have formed the following data:
Probabilty that Team 0 wins is P(Y=0) = .65

Probability that Team 1 wins is P(Y=1) = 1 – P(Y=0) = 0.35

Probabilty that Team 1 wins the match it hosted = P(X=1|Y=1| = 0.75

Probability that Team 1 hosted the match win by Team 0 = P(X=1|Y=0) =0.3

P(X=1|Y=0) = P(X=1|Y=1) = ?
Tell me whether the last statement is correct or not. Book has written following:
Our objective is to compute P(Y =1 l X = 1), which is the conditional
probability that Team 1 wins the next match it will be hosting, and compares
it against P(Y=0 l X= 1).
They have written the Y first , I have written the X first.

Please guide me.

Thanks for your help.

Zulfi.

 

Hi,
I am trying to solve your Q:
Team 0 and Team 1 have played 1000 games and Team 0 has won 900 of them.
When the two teams play next, knowing only this information, which team is more likely to win?

Probability of Team 1 winning = 100/1000 = 0.1
Probability of Team 2 winning = 900/1000 = 0.9
Probability of Team 1 losing = 900/1000 = 0.1
Probability of Team 2 losing = 100/1000 = 0.1

Let X represents the Probability of Team winning the match
Let Y represents the Probability of Team losing the match

P(X=1|Y=0) = P(X=0|Y=1)

Kindly guide me if the above approach is correct or not.

Zulfi.

 

Hi,
Kindly tell me the difference between:
P(X=1 | Y=1) & P(Y=1 | X=1)?

P(X=1 | Y=1) = Conditional Probability of Hosting match by Team 1 given the probability of Team 1 winning the match
P(Y=1 | X=1) = Conditional Probability of winning match by Team 1 given the probability of Team 1 hosting the match

Is the above correct? This means that P(X= 1 | Y=1) and P(Y=1 | X =1) are different?
Please guide me.

Book says this:
Our objective is to compute P(Y = l | x = 1), which is the conditional
probability that Team 1 wins the next match it will be hosting, and compares
it against P(Y =0 | X= 1). However they are evaluating following:

P(X=1) * P(Y= l | x = 1) = P(X = l | Y =1) x P(Y = 1)

Please guide me is the above correct?

Zulfi.