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Probability- another one

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Senior | Next Rank: 100 Posts
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by Nidhs » Fri Feb 08, 2008 6:06 pm
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 ans is [c] but i do'nt know how to solve it. Can somebody help me
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by gmatguy16 » Sat Feb 09, 2008 9:28 am
is there a typo in the question ,are the number of horses 5.if there are 5 horses answer is 61/125.
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by gmatguy16 » Sat Feb 09, 2008 9:30 am
actually number of horses are 5 ..missed that part 4 other horses....
approach is that he goes back with money in his pocket if he wins atleast one race = 1 - winnning none of the races =
1-((4/5)*(4/5)*(4/5))=61/125
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by xilef » Wed Feb 13, 2008 4:12 pm
What's wrong with this approach?

P of winning at least 1 game =

(P of winning 1st race * P of not winning 2nd * P of not winning 3rd) + (P of not winning 1st * P of winning 2nd * P of not winning 3rd) + (P of not winning 1st * P of not winning 2nd * P of winning 3rd) =

(1/5*4/5*4/5) + (4/5*1/5*4/5) + (4/5*4/5*1/5) = 48/125
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by subbu123 » Wed Feb 13, 2008 5:28 pm
Hi xilef,

Your approach is also correct. However you missed four more cases

winning at least 2 (4/125 + 4/125 + 4/125) + winning all the three races(1/125)

This approach takes more time. Take the oppsite 1-P(winning none)
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by xilef » Thu Feb 14, 2008 2:12 pm
Right, for some reason didn't pay attention to the fact that it is a P of winning ATLEAST one not just one.
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