sorry to be a pain, please check

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Melissa79

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Two teams(Comets and Barons) are evenly matched. They play a best out of three game series.

The probability that one of the team wins 2 straight games is 2/6

The probability that one team wins is 1/2.

The probability the comets win the first 2 games is 1/6.

The probability that comets win at least one game is 5/6.

The probability that the comets win the last 2 games is 1/6.

This seems easy enough ,but what I am worried about is if I multiply the branches on a tree diagram it gives me different results. Example, The probability that the Comets win the first two games comes out 1/4. Which is it?
 
I will use "B" and "C" to stand for "Barons win" and "Comets win", respectively, where "win" here refers to a game in the "two out of three games" in the three-game series.

1) probability that one of the team wins 2 straight games

Possible outcomes: BBB, BBC, BCB, BCC, CBB, CBC, CCB, and CCC. Of these, only BBC, BCC, CBB, and CCB include exactly two wins in a row.

2) probability that one team wins

I'm not sure what this means. Are they referring here to the entire three-game series? Then there is a 100% chance that "one team" wins, because somebody has to win. (There can't be a tie, because it's "two out of three" to win the series.)

I would ask for clarification, or say "1", for "100%".

3) probability the comets win the first 2 games

See the listing in (1) above. Divide the number of outcomes containing two C's from the total number of outcomes.

4) probability that comets win at least one game

See the listing in (1) above.

5) probability that the comets win the last 2 games

See the listing in (1) above.

Since I'm not familiar with what you mean by "multiplying branches of a tree diagram", and since I don't know the steps or reasoning you're using to get your various answers, I'm afraid I can't comment on that.

Eliz.
 
Stapel seems to have covered it quite well. Just know that you're no more a pain than I am....lol. I am constantly asking for help, but hey, that's what the forum is for, right? So as long as you are willing to help yourself out, we don't mind helping you out.
 
Sorry 'bout that. Ya caught me up a tree. The real table is
WW(W),WW(L),LL(W),LL(L),WLW,LWW,WLL,LWL
(?) are games that weren't played but have to be included in the table 'cause if they had been they would have contributed to the odds.

The probability that the comets win 2 straight games is 3/8
The probability that the Barons win 2 straight games is 3/8
The probability that one of the team wins 2 straight games is 6/8

The probability that the comets win is 4/8.
The probability that the Barons win is 4/8.
The probability that one team wins is 1.

The probability the comets win the first 2 games is 2/8.

The probability that comets win at least one game is 7/8.
The probability that the comets win the last 2 games is 3/8.

I didn't see Staples. I'm a very slow typist.
Re #1 Staple didn't include BBB & CCC. I think she should have.
 
Heres the problem with that Gene, my professor said there are only 6 outcomes not 8 when I asked him. So now what do you think?
 
Melissa79 said:
...my professor said there are only 6 outcomes not 8....
Click to expand...
Ooo, hadn't thought of that: In a "best two of three" series, if the other guy has won the first two, do you bother with the last game?

So the outcomes are actually BB, BCB, BCC, CBB, CBC, and CC.

Eliz.
 
I still think my answers are correct. The WW occurs 1 out of 4 times (1/2*1/2). If you consider six outcomes you have to count WW & LL each twice as likely as WLW which still makes the denominators 8, not 6.
How do they work in your tree? It did repair the one you mentioned.
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Gene
 
Im confused.my tree diagram has these numbers at the end of each branch 1/4 +1/8+1/8+1/8+1/8+1/4 which equals 1 as it should but the professor said six outcomes so I do not know what to do. This little project is 20% of my final grade for the class and is due tuesday
 
You have six outcomes on your tree which is what He wanted. The denominator of 8 doesn't affect that. The tips of the branches are good.
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Gene
 
They are over 8. That is the way the tree branches work out.
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Gene
 
No. If you flip a bent coin that comes up heads twice as often as tails there are two outcomes, heads or tails. Heads = 2/3, tails = 1/3. The 3 doesn't mean there are three outcomes.
 
How about a seven sided die? Two outcomes, even or odd. Even = 3/7, odd = 4/7
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Gene
 
I guess my confusion is the F/N rule which is the probability of an event is the event divided by the total outcomee. Example would be a dice landing on 2. Which is 2/6 which is 1/3. I thought this idea worked into my original problem.
 
Actually it is 1/6 for a 2.

I don't have the rule in front of me but if you do, look at it again. There must be a caviat about what constitutes an outcome that my counter examples (and this project) violates. Maybe Staple will be back. She is better than I am with that sort of thing. I can only say I believe in my numbers.
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Gene
 
I just wanted to thank you Gene for all your help it has been appreciated, believe me. I did write a private message to Staple asking her to look over everything. Hopefully she will. It's funny I work part time at an elementry school. I asked a few of the teachers about this problem and they were not sure if it was over 6 or 8 lol. The vice principal of the school is going to look over it and tell me what he thinks Monday. I guess I am analyzing this to death. I have a low B in my statistics class right now so this project may make or break my grade for the semester. Any other feedback will be appreciated. If I do well I will be sure to thank again.
 
You might want to brouse
http://www.mathleague.com/help/percent/percent.htm
Notice the difference between events and outcomes (though it seems to me that they mix them up too), especially with the bags of marbles. Think about them being numbered as well as colored. The numbers would be events, the colors outcomes. It doesn't quite match this contest. I still can't rationalize WW being two events without considering the third (unplayed) game though deep in my heart I'm sure it is.
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Gene
 
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