4. Probability
Basic Concepts of Probability
1:11 minutesProblem 4.1.43a
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.
a. How much net profit was made from a $2 win bet on Justify?
Verified step by step guidance1
Identify the total payout from the winning ticket, which is $7.80, and the initial bet amount, which is $2.
Understand that the net profit is calculated by subtracting the initial bet amount from the total payout.
Write the formula for net profit: Net Profit = Total Payout - Initial Bet.
Substitute the given values into the formula: Net Profit = $7.80 - $2.
Simplify the expression to find the net profit, which represents the amount earned beyond the initial bet.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Net Profit
Net profit is the amount of money gained after subtracting the initial investment from the total returns. In betting, it is calculated by taking the winnings and deducting the amount wagered. For example, if a bettor wins $7.80 from a $2 bet, the net profit would be $7.80 - $2 = $5.80.
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Betting Odds
Betting odds represent the likelihood of a particular outcome occurring and determine how much a bettor can win. In this case, the odds for Justify winning were such that a $2 bet returned $7.80, indicating a favorable outcome. Understanding odds helps bettors assess potential returns and risks associated with their wagers.
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Return on Investment (ROI)
Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment. It is calculated by dividing the net profit by the initial investment and multiplying by 100 to get a percentage. In this scenario, the ROI from the $2 bet on Justify can help bettors understand the profitability of their wager relative to the amount they risked.
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