Question

Belmont Stakes.The Belmont Stakes is the third leg, after the Kentucky Derby and Preakness Stakes, of the Triple Crown of thoroughbred horseracing. The morning-line betting odds of the two favorites, Orb and Revolutionary, for the 2013 Belmont Stakes were 7 to 2 (against) and 5 to I (against), respectively. Based on the morning-line betting odds, determine the probability that the winner of the race would be

(a) Orb. (b) Revolutionary.

Short answer

Part (a) 0.4

Part (b) 0.167

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

The Belmont Stakes is the third leg, after the Kentucky Derby and Preakness Stakes, of the Triple Crown of thoroughbred horseracing. The morning-line betting odds of the two favorites, Orb and Revolutionary, for the 2013 Belmont Stakes were 7 to 2 (against) and 5 to I (against), respectively.

Part (a) Step 2. Calculate the probability that Orb will win the race based on the morning-line betting odds.

It's worth noting that Orb's morning-line betting odds are 7 to 2. (against).

The ratio given below determines the likelihood of winning at odds:

$\frac{1-p}{p}$

Therefore,

$$\begin{gathered} \frac{1-p}{p}=\frac{7}{2} \\ 2\left(1-p\right)=7p \\ 2-2p=7p \\ 2=5p \\ \frac{2}{5}=p \\ p=0.4 \end{gathered}$$

Part (b) Step 1. Calculate the probability that Revolutionary will win the race based on the morning-line betting odds.

It's worth noting that Revolutionary's morning-line betting odds are 5 to 1. (against).

Therefore, the probability is:

$$\begin{gathered} \frac{1-p}{p}=\frac{5}{1} \\ 1\left(1-p\right)=5p \\ 1-p=5p \\ 1=6p \\ \frac{1}{6}=p \\ p=0.167 \end{gathered}$$