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. $101/420$
• B. $101/210$
• C. $319/420$
• D. $111/420$

Answer 1

The correct option is C $319/420$

Given, 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, $P\left(A\right)=\frac{1}{4}$

The probability of winning the horse B, $P\left(B\right)=\frac{1}{5}$

The probability of winning the horse C, $P\left(C\right)=\frac{1}{6}$

The probability of winning the horse D, $P\left(D\right)=\frac{1}{7}$
The probability that one of the horse winning the race $=\left(P\right(A)+P(B)+P(C)+P(D\left)\right)$
$=(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7})$

$=\frac{(210+168+140+120)}{840}=\frac{319}{420}$