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A certain sports league has ten teams in its Western Confere

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A certain sports league has ten teams in its Western Confere [#permalink] New post 30 Sep 2012, 17:10
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Question Stats:

75% (02:25) correct 25% (03:07) wrong based on 8 sessions
A certain sports league has ten teams in its Western Conference and eight teams in its Eastern Conference. At the end of the season, two teams, one from each conference, play in The Big Game. Two teams in each conference are located in Texas. If each team in each conference has an equal probability of making it to The Big Game, and if each team in The Big Game has an equal probability of winning that game, what is the probability that a team from Texas will win The Big Game?

a) 3/20
b) 2/9
c) 9/40
d) 27/80
e) 5/16

What would be the probability of P{East winning the Super bowl}. Is it 1/2? Or 8/18 because of equally likely probabilities?

Just curious. Here's why I am asking:

Here's what I did initially:
P(T=texas wins) = P(Texas Wins/East) P(East) + P (Texas Wins/West) P(West)
= 10/18 * 2/10 + 8/18 * 2/8
= 2/9

If I change P(Texas Wins/East) = P(Texas Wins/East) = 1/2, ( the question says that "If each team in each conference has an equal probability of making it to The Big Game, and if each team in The Big Game has an equal probability of winning that game," --- I am not sure whether this is an accurate translation...)

then P(texas wins) = 1/2 * 2/10 + 1/2 * 2/8 = 9/40... Any thoughts? Please help....
[Reveal] Spoiler: OA
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Re: A certain sports league has ten teams in its Western Confere [#permalink] New post 30 Sep 2012, 22:08
voodoochild wrote:
A certain sports league has ten teams in its Western Conference and eight teams in its Eastern Conference. At the end of the season, two teams, one from each conference, play in The Big Game. Two teams in each conference are located in Texas. If each team in each conference has an equal probability of making it to The Big Game, and if each team in The Big Game has an equal probability of winning that game, what is the probability that a team from Texas will win The Big Game?

a) 3/20
b) 2/9
c) 9/40
d) 27/80
e) 5/16

What would be the probability of P{East winning the Super bowl}. Is it 1/2? Or 8/18 because of equally likely probabilities?

Just curious. Here's why I am asking:

Here's what I did initially:
P(T=texas wins) = P(Texas Wins/East) P(East) + P (Texas Wins/West) P(West)
= 10/18 * 2/10 + 8/18 * 2/8
= 2/9

If I change P(Texas Wins/East) = P(Texas Wins/East) = 1/2, ( the question says that "If each team in each conference has an equal probability of making it to The Big Game, and if each team in The Big Game has an equal probability of winning that game," --- I am not sure whether this is an accurate translation...)

then P(texas wins) = 1/2 * 2/10 + 1/2 * 2/8 = 9/40... Any thoughts? Please help....


Following are the three cases
1. Texas team from West, no Texas team from East and Texas team wins = 2/10 * 6/8 *1/2 = 3/40
2. No Texas team from West, Texas team from East and Texas team wins = 8/10 * 2/8 *1/2 = 4/40
3. Texas team from West, Texas team from East (since both are texas teams and one will win, this is certain event) = 2/10 * 2/8 = 2/40
Hence, the required probability = 3/40+4/40+2/40 = 9/40
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Re: A certain sports league has ten teams in its Western Confere [#permalink] New post 01 Oct 2012, 03:19
thanks. That's another way to solve the problem. Do you think that my solution is incorrect? Thoughts?
Re: A certain sports league has ten teams in its Western Confere   [#permalink] 01 Oct 2012, 03:19
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