Probability- another one

[Nidhs]

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

[gmatguy16]

is there a typo in the question ,are the number of horses 5.if there are 5 horses answer is 61/125.

[gmatguy16]

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

[xilef]

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

[subbu123]

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)

[xilef]

Right, for some reason didn't pay attention to the fact that it is a P of winning ATLEAST one not just one.