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Question

# In a given race, the odds in favour of four horses A,B,C & D are 1:3,1:4,1:5 and 1:6 respectively. Assuming that a dead heat is impossible, find the chance that one of them wins the race

A
101/420
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B
101/210
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C
319/420
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D
111/420
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Solution

## The correct option is C 319/420Given, Odds in favour of four horses A,B,C,D are 1:3,1:4,1:5,1:6.The probability of winning the horse A, P(A)=14The probability of winning the horse B, P(B)=15The probability of winning the horse C, P(C)=16The probability of winning the horse D, P(D)=17The probability that one of the horse winning the race =(P(A)+P(B)+P(C)+P(D))=(14+15+16+17)=(210+168+140+120)840=319420

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