win win problem

Apr 2010
160
0
dfsdfdf
Dear Sir,
I need help some help with the below problem and would appreciate very much if can offer some help.
thanks
Kingman

1) In a match, 2 teams (A and B) will play each other in the best of 3 games. That is, the final team to win 2 games will be the winner. In the first games, both teams have equal chance of winning. In subsequent games, the probability of team A winning team B given that team A won in the previous game is p and the probability of team A winning team B given that team A lost in the previous game is 1/3.

Find the value of p such that the team A has equal chances of winning and losing the competition.

Answer(2/3)
 

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MHF Hall of Honor
Mar 2010
2,340
821
Chicago
Dear Sir,
I need help some help with the below problem and would appreciate very much if can offer some help.
thanks
Kingman

1) In a match, 2 teams (A and B) will play each other in the best of 3 games. That is, the final team to win 2 games will be the winner. In the first games, both teams have equal chance of winning. In subsequent games, the probability of team A winning team B given that team A won in the previous game is p and the probability of team A winning team B given that team A lost in the previous game is 1/3.

Find the value of p such that the team A has equal chances of winning and losing the competition.

Answer(2/3)
Have you tried this on your own? You can draw a decision tree, maybe known to you as a probability tree. You will need to write an equation and solve for p.
 
May 2010
25
0
The probability tree would give you all you need and you just start from the beginning and work your way down.
 
Apr 2010
160
0
dfsdfdf
this is exactly my difficulty lies

Dear oregon88,
Thanks very much for your reply. I have great difficulty in drawing my tree diagram.

Here is my difficulty:
A either win or lose and
B either win or lose but the question only mention winning: from here I am stuck !
How to draw the tree giving all the outcomes is my problem.
please help
thanks

http://www.mathhelpforum.com/math-help/members/oregon88.html
 

undefined

MHF Hall of Honor
Mar 2010
2,340
821
Chicago
Dear oregon88,
Thanks very much for your reply. I have great difficulty in drawing my tree diagram.

Here is my difficulty:
A either win or lose and
B either win or lose but the question only mention winning: from here I am stuck !
How to draw the tree giving all the outcomes is my problem.
please help
thanks
P(win) = 1 - P(lose)
P(lose) = 1 - P(win)

This is because the probabilities for all possible outcomes must always add up to 1. (As in, 100%)

Does that help?
 
Apr 2010
160
0
dfsdfdf
thanks,
I know this fact but still need to know how the tree diagram look which depicts the win and lose of both A and B.
This does not look like a typical tree diagram.
Please help!
 

undefined

MHF Hall of Honor
Mar 2010
2,340
821
Chicago
thanks,
I know this fact but still need to know how the tree diagram look which depicts the win and lose of both A and B.
This does not look like a typical tree diagram.
Please help!
Hmm, the diagram is typical enough if you ask me. I don't know if you're used to going up to down, but I generally go left to right. Attached. (It's kind of ugly since it's with MS Paint/mouse.) Overall win for A is marked in green, otherwise blue.
 

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