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Question

(A) Let the probabilities of horses $A$,$B$,and $C$ winning be $a$,$b$,and $c$ respectively.Since one of them must win,the sum of their probabilities

Vedclass · Accepted Answer

$\frac{4}{7}, \frac{2}{7}, \frac{1}{7}$

Vedclass · Answer

(A) Let the probabilities of horses $A$,$B$,and $C$ winning be $a$,$b$,and $c$ respectively.Since one of them must win,the sum of their probabilities is $a + b + c = 1$ ... $(i)$Given that $a = 2b$ and $b = 2c$.Substituting $b = 2c$ into the expression for $a$,we get $a = 2(2c) = 4c$.Now,substitute $a = 4c$ and $b = 2c$ into equation $(i)$:$4c + 2c + c = 1$$7c = 1$$c = \frac{1}{7}$Now,find $b$ and $a$:$b = 2c = 2 	imes \frac{1}{7} = \frac{2}{7}$$a = 2b = 2 	imes \frac{2}{7} = \frac{4}{7}$Therefore,the probabilities of horses $A$,$B$,and $C$ winning are $\frac{4}{7}, \frac{2}{7}, \frac{1}{7}$ respectively.

$A$,$B$,$C$ are three horses participating in a race. The probability of horse $A$ to win the race is twice that of horse $B$ and the probability of horse $B$ to win is twice that of horse $C$. Then the probabilities of horses $A$,$B$,and $C$ to win the race are respectively:

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