Final answer:
To make a fair bet with odds against a horse at 5 to 2 and a $14 win, the correct amount to bet would be $5.60. This is calculated using the ratio of potential profit to the bet amount, adjusted to the odds of the event happening.
Step-by-step explanation:
The question involves calculating a fair bet amount based on given odds against a horse winning a race. To answer this, we need to understand the concept of 'fair game' and odds.
The odds against the horse are 5 to 2, which means for every 2 times the horse is expected to win, it is expected to lose 5 times. To make the betting game fair, the ratio of the potential profit to the amount bet should be equal to the odds of winning.
Now, let's find the fair bet amount that corresponds to a $14 win. Given the odds 5:2 against winning, we can create the equation 14 / x = 5 / 2, where x is the amount to bet.
Cross-multiplying gives us 28 = 5x, thus x = 28 / 5, which simplifies to $5.60.
Therefore, the fair bet amount in this scenario is $5.60.