If the odds in favor of Fast Leg winning a horse race are 9 to 7 and the first prize is , what is the expected value
of Fast Leg’s winnings?
The expected value is .

Ask by Ross Park. in the United States

Jan 23,2025

Question

If the odds in favor of Fast Leg winning a horse race are 9 to 7 and the first prize is $$ \$ 112,000 $$, what is the expected value of Fast Leg's winnings? The expected value is $$ \$ \square $$.

UpStudy AI · Accepted Answer

To calculate the expected value of Fast Leg's winnings, follow these steps:

1. **Determine the Probability of Winning:**
   
   The odds in favor of Fast Leg winning are 9 to 7. This means:
   
   $$
   \text{Probability of winning} = \frac{9}{9 + 7} = \frac{9}{16}
   $$
   
2. **Determine the Probability of Losing:**
   
   $$
   \text{Probability of losing} = 1 - \frac{9}{16} = \frac{7}{16}
   $$
   
3. **Calculate the Expected Value:**
   
   Assuming that if Fast Leg loses, the winnings are \$0, the expected value $$ E $$ is:
   
   $$
   E = \left(\frac{9}{16}\right) \times \$112,000 + \left(\frac{7}{16}\right) \times \$0 = \frac{9}{16} \times \$112,000
   $$
   
   $$
   E = \frac{9 \times 112,000}{16} = \frac{1,008,000}{16} = \$63,000
   $$
   
**The expected value is \$63,000.**
The expected value of Fast Leg's winnings is \$63,000.

If the odds in favor of Fast Leg winning a horse race are 9 to 7 and the first prize is , what is the expected value
of Fast Leg’s winnings?
The expected value is .

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If the odds in favor of Fast Leg winning a horse race are 9 to 7 and the first prize is , what is the expected value of Fast Leg’s winnings? The expected value is .