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 calculate the expected value, we need to find the probabilities of Fast Leg winning and losing. Given the odds of 7 to 3, the probability of winning is \( \frac{7}{7+3} = \frac{7}{10} = 0.7 \) and the probability of losing is \( \frac{3}{10} = 0.3 \). The expected value can be calculated by multiplying the prize by the probability of winning and subtracting the loss (which is the prize multiplied by the probability of losing): \( EV = (0.7 \times 30,000) + (0.3 \times 0) = 21,000 + 0 = 21,000 \). So, the expected value is \( \$ 21,000 \). When considering expected value in betting situations like this, it's important to remember how the odds factor in actual payouts. If you were to place a bet, making sure you understand the returns versus the risks can be crucial in making informed decisions. Always calculate your potential outcomes before placing that bet!