If the odds in favor of Fast Leg winning a horse race are 7 to 3 and the first prize is \( \$ 30,000 \), what is the expected value of Fast Leg's winning 0 of 1 The expected value is \( \$ \square \)

To determine the expected value of Fast Leg's potential winnings, let's break down the information provided: 1. **Odds in Favor of Winning:** - The odds are 7 to 3. - This means for every 7 chances of winning, there are 3 chances of losing. 2. **Probability Calculations:** - **Probability of Winning (P(win))** = \( \frac{7}{7 + 3} = \frac{7}{10} = 0.7 \) - **Probability of Losing (P(lose))** = \( 1 - P(win) = 1 - 0.7 = 0.3 \) 3. **Monetary Outcomes:** - **Winning:** Fast Leg wins \$30,000. - **Losing:** Fast Leg wins \$0. 4. **Expected Value (EV) Calculation:** \[ EV = (P(win) \times \text{Winning Amount}) + (P(lose) \times \text{Losing Amount}) \] Plugging in the numbers: \[ EV = (0.7 \times \$30,000) + (0.3 \times \$0) = \$21,000 + \$0 = \$21,000 \] **Therefore, the expected value of Fast Leg's winning is \$21,000.** \$\mathbf{21,\!000}