Kentucky Derby Odds When the horse Justify won the 144th Kentucky...

4. Probability

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

2:14 minutes

Problem 4.1.43c

Textbook Question

Kentucky Derby Odds When the horse Justify won the 144th Kentucky Derby, a $2 bet on a Justify win resulted in a winning ticket worth $7.80.

c. If the payoff odds were the actual odds found in part (c), what would be the worth of a $2 win ticket after the Justify win?

Verified step by step guidance

Step 1: Understand the problem. The question asks us to calculate the worth of a $2 win ticket based on the payoff odds provided in part (c). Payoff odds represent the ratio of the net profit to the original bet amount.

Step 2: Recall the formula for calculating the total worth of a winning ticket: Total Worth = Original Bet + (Original Bet × Payoff Odds).

Step 3: Substitute the given values into the formula. The original bet is $2, and the payoff odds are provided in part (c) (you would need to refer to the odds from part (c) to proceed).

Step 4: Perform the multiplication to calculate the net profit: Multiply the original bet ($2) by the payoff odds to find the profit.

Step 5: Add the original bet amount ($2) to the calculated profit to determine the total worth of the winning ticket.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Payoff Odds

Payoff odds represent the amount of money a bettor receives in return for a winning bet, relative to the amount wagered. In this case, the payoff odds for a $2 bet on Justify winning were $7.80, meaning the bettor receives $7.80 for every $2 wagered. Understanding payoff odds is crucial for calculating potential returns on bets.

Betting Odds

Betting odds indicate the probability of a particular outcome occurring, often expressed in fractional or decimal form. They help bettors assess the risk and potential reward of their wagers. In the context of the Kentucky Derby, knowing the odds can inform decisions on how much to bet and which horses to back.

Expected Value

Expected value is a statistical concept that calculates the average outcome of a bet if it were placed multiple times. It is determined by multiplying the probability of each outcome by its respective payoff and summing these products. Understanding expected value helps bettors make informed decisions by evaluating whether a bet is worth the risk based on potential returns.

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Kentucky Derby Odds When the horse Justify won the 144th Kentucky Derby, a $2 bet on a Justify win resulted in a winning ticket worth $7.80.c. If the payoff odds were the actual odds found in part (c), what would be the worth of a $2 win ticket after the Justify win?