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Jim goes to the track with $150 in his pocket

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Jim goes to the track with $150 in his pocket  [#permalink]

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New post 15 Apr 2018, 21:52
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:19) correct 36% (02:00) wrong based on 74 sessions

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Jim goes to the track with $150 in his pocket. His favorite horse, Major, is running three races against four other horses. Each competing horse has an equal chance of winning and Jim bets in all three races, $50 per race. What is the probability of Jim leaving the track with money in his pocket?

(A) 1/125

(B) 1/5

(C) 61/125

(D) 64/125

(E) 4/5
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Re: Jim goes to the track with $150 in his pocket  [#permalink]

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New post 16 Apr 2018, 03:11
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praveenbaranwal wrote:
Jim goes to the track with $150 in his pocket. His favorite horse, Major, is running three races against four other horses. Each competing horse has an equal chance of winning and Jim bets in all three races, $50 per race. What is the probability of Jim leaving the track with money in his pocket?

(A) 1/125

(B) 1/5

(C) 61/125

(D) 64/125

(E) 4/5

Solution
Here the tricky part is "Major, is running three races against four other horses"
So, in total there are 5 horses.
If Jim goes back with money in his pocket, then he must have won at least one race = 1 - (Winning none of the races)
= 1-((4/5)*(4/5)*(4/5))=61/125
Option C
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Jim goes to the track with $150 in his pocket  [#permalink]

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New post 16 Apr 2018, 23:41
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praveenbaranwal wrote:
Jim goes to the track with $150 in his pocket. His favorite horse, Major, is running three races against four other horses. Each competing horse has an equal chance of winning and Jim bets in all three races, $50 per race. What is the probability of Jim leaving the track with money in his pocket?

(A) 1/125

(B) 1/5

(C) 61/125

(D) 64/125

(E) 4/5



The question stem has the following information
1. Major is running three races with four other horses(Total : 3 races - 5 horses/race)
2. What is the probability that Jim leaves the track with money (Probability he doesn't lose all 3 races)

The probability of Major losing
  • one of the races is \(\frac{4}{5}\)
  • all 3 races is \((\frac{4}{5})^3 = \frac{64}{125}\)

Therefore, the probability that Jim leaves the track with money is 1 - P(Major losing all 3 races) = \(1 - \frac{64}{125} = \frac{61}{125}\) (Option C)
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Re: Jim goes to the track with $150 in his pocket  [#permalink]

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New post 29 Apr 2018, 07:07
1-(4*4*4/5*5*5)
=1-64/125
=61/125

Here 4/5 is probability of not winning game as there are 5 horses in total.

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Re: Jim goes to the track with $150 in his pocket  [#permalink]

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New post 31 Mar 2019, 20:49
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I did it the other way.
If Jim will take back money, his horse will either win one game, two games or all 3 games.
P(1 game) = 1/5*4/5*4/5*3 ( Since this can happen in 3 different ways) = 48/125
P( 2 games) = 1/5*1/5*4/5*3 = 12/125
p(3 games) = 1/5*1/5*1/5 = 1/125

Adding all 3 probabilities = 48/125 + 12/125 + 1/125 = 61/125
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Re: Jim goes to the track with $150 in his pocket   [#permalink] 31 Mar 2019, 20:49
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