probability question

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probability question

by sana.noor » Mon Aug 05, 2013 10:06 am
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

OA is C
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by [email protected] » Mon Aug 05, 2013 11:50 am
Hi sana.noor,

This is a layered probability question with lots of details that you'd need to keep track of.

Here's one way to solve it:

First, since it's a probability question, let's figure out the total possible outcomes:

Western Conference: 10 teams
Eastern Conference: 8 teams
Each Conference has 2 teams from Texas (we'll deal with this later)
10 x 8 = 80 possible Championship Games


A team can either win or lose the Championship Game
80 x 2 = 160 possible Championship Game outcomes

The question requires at least 1 Texas Team WIN the championship game, so let's figure out the ways for a team to get to the game AND win.
Each of the 2 Texas teams in the East could play each of the 8 non-Texas teams in the West: that's 16 possible wins
Each of the 2 Texas teams in the East could play each of the 2 Texas teams in the West: that's 8 possible wins (since all teams are from Texas)
Each of the 6 non-Texas teams in the East could play each of the 2 Texas teams in the West: that's 12 possible wins
Total Texas wins = 16 + 8 + 12 = 36

Total possible Texas wins/Total possible wins = 36/180 = 9/40

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