Horse Name Odds of Placing in the top three The Baron H

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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

by varun289 » Fri Apr 05, 2013 11:52 am

Horse Name

Odds of Placing in the top three
The Baron 3/5

Happy Cynic 7/10

California Girl 3/4

Love Song 1/4

Inamorata 1/2

The chart above lists the odds that a horse will place in the top three. As part of a contest, if at least 2 of the horses that a person bets upon finish in the top three, the bettor receives a T-shirt. If Cecilia bets on The Baron, Happy Cynic, and Inamorata, what is the probability that she does not receive a T-shirt?

6/100 , 21/100 , 29/100 , 35/100., 65/100

i wonder why not to include the case when all 3 lost combination with only 2 lost one wins

IMO - 35/100 while its 29 ????

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Source: Beat The GMAT — Problem Solving | Fri Apr 05, 2013 11:52 am

misterholmes: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Wed Dec 16, 2009 11:57 am; Location: New York & Rotterdam; Thanked: 9 times; GMAT Score:780

by misterholmes » Sat Apr 06, 2013 9:27 am

She loses in the case when none of her horses place, and in the cases when only one place. So I would just add probability chains.
None place: 2*3*1 6/100
Baron only: 3*3*1 9/100
Happy only: 2*7*1 14/100
Inamo only: 2*3*1 6/100

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by GMATGuruNY » Sat Apr 06, 2013 5:41 pm

varun289 wrote:Horse Name

Odds of Placing in the top three
The Baron 3/5

Happy Cynic 7/10

California Girl 3/4

Love Song 1/4

Inamorata 1/2

The chart above lists the odds that a horse will place in the top three. As part of a contest, if at least 2 of the horses that a person bets upon finish in the top three, the bettor receives a T-shirt. If Cecilia bets on The Baron, Happy Cynic, and Inamorata, what is the probability that she does not receive a T-shirt?

6/100 , 21/100 , 29/100 , 35/100., 65/100

The problem should make clear that ONLY the 5 horses listed in the chart are competing in the race.

If the two horses that Cecilia does NOT choose -- California Girl and Love Song -- both finish in the top 3, then one of the 3 horses that Cecilia does choose -- The Baron, Happy Cynic, and Inamorata -- must also finish in the top 3, since a total of 3 horses must finish in the top 3.
Thus, it is not possible that NONE of the horses that Cecilia chooses finishes in the top 3.
As a result, only 3 cases are possible:
Case 1: Of The Baron, Happy Cynic, and Inamorata, EXACTLY 1 wins.
Case 2: Of The Baron, Happy Cynic, and Inamorata, EXACTLY 2 win.
Case 3: Of The Baron, Happy Cynic, and Inamorata, ALL 3 win.

Only in Case 1 does Cecilia NOT win a t-shirt.

Case 1: Of The Baron, Happy Cynic, and Inamorata, EXACTLY 1 wins.
P(THE BARON WINS, Happy Cynic loses, and Inamorata loses) = 3/5 * 3/10 * 1/2 = 9/100.
P(The Baron loses, HAPPY CYNIC WINS, and Inamorata loses) = 2/5 * 7/10 * 1/2 = 14/100.
P(The Baron loses, Happy Cynic loses, and INAMORATA WINS) = 2/5 * 3/10 * 1/2 = 6/100.
Since any of these outcomes will result in Cecilia's not winning a t-shirt, we ADD the fractions:
9/100 + 14/100 + 6/100 = 29/100.

The correct answer is C.

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