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15 Apr 2018, 21:52
6
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:16) correct 36% (01:58) wrong based on 80 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
Manager
Joined: 03 Mar 2018
Posts: 206

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16 Apr 2018, 23:41
1
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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Director
Joined: 02 Oct 2017
Posts: 720

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31 Mar 2019, 20:49
1
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