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Question

In a race, the odds in favour of horses A, B, C, D are 1 : 3, 1 : 4, 1 : 5 and

1 : 6 respectively. Find probability that one of them wins the race.


Solution

We have,

P(A):P(¯¯¯¯A)=1:3

P(A)=14

P(B):P(¯¯¯¯B)=1:4

P(B)=15

P(C):P(¯¯¯¯¯¯¯¯CB)=1:5

P(C)=16

P(D):P(¯¯¯¯¯D)=1:6

P(D)=17

Probability that at least one of them wins is given by

P(ABCD)

=P(A)+P(B)+P(C)+P(D)

=14+15+16+17=319420

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