sports league

[CSASHISHPANDAY]

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 and source after discussion

[CSASHISHPANDAY]

here is an answer of the question https://www.beatthegmat.com/probability- ... 86396.html

but i m unable to understand how the probability of Texas team reaches final from West,p(w)is 2/10.

[niketdoshi123]

but i m unable to understand how the probability of Texas team reaches final from West,p(w)is 2/10.

Two teams in each conference are located in Texas
So 2 out of 10 teams in Western Conference are located in Texas

Also, each team in each conference has equal probability of making it to The Big Game.
So probability that a team in western conference makes it to the final = 1/10

Since there are two teams from Texas, required probability = 2*1/10

[GMATGuruNY]

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 and source after discussion

Case 1: A Western team from Texas wins
P(a Western team from Texas is in the Big Game) = 2/10. (Of the 10 Western teams, 2 are from Texas.)
P(this team wins) = 1/2. (Since each team in the Big Game has an equal chance of winning.)
Since we want both of these events to happen, we multiply the fractions:
2/10 * 1/2 = 1/10.

Case 2: An Eastern team from Texas wins
P(an Eastern team from Texas is in the Big Game) = 2/8. (Of the 8 Eastern teams, 2 are from Texas.)
P(this team wins) = 1/2. (Since each team in the Big Game has the same chance of winning.)
Since we want both of these events to happen, we multiply the fractions:
2/8 * 1/2 = 1/8

Since either case will yield a favorable outcome,we ADD the probabilities:
1/10 + 1/8 = 4/40 + 5/40 = 9/40.

The correct answer is C.