In Las Vegas, a particular sports bet has about a $30 \%$ chance of winning. If the bet wins, the bettor will win 15 dollars. If the bet loses, the bettor will lose 10 dollars.

The expected return of placing one of these bets is -2.50 dollars.
Which of the following statements are true?
Choose all answers that apply:
A It is possible for a bettor to place 2 of these bets and win both of them.

B The average return per bet from 2 of these bets must be exactly -2.50 dollars.
c If a bettor places a large number of these bets, they should expect to average a return of about -2.50 dollars per bet.

Question

In Las Vegas, a particular sports bet has about a $30 \%$ chance of winning. If the bet wins, the bettor will win 15 dollars. If the bet loses, the bettor will lose 10 dollars.

The expected return of placing one of these bets is -2.50 dollars.
Which of the following statements are true?
Choose all answers that apply:
A It is possible for a bettor to place 2 of these bets and win both of them.

B The average return per bet from 2 of these bets must be exactly -2.50 dollars.
c If a bettor places a large number of these bets, they should expect to average a return of about -2.50 dollars per bet.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the expected return for one bet using the probabilities and outcomes given: $0.3 imes 15 + 0.7 imes (-10)$. ‖ ‖ step 2 ⋮ Simplify the calculation: $4.5 - 7 = -2.5$. ‖ ‖ step 3 ⋮ Recognize that statement A is about the possibility of an event, which is not related to the expected value. ‖ ‖ step 4 ⋮ Understand that statement B is incorrect because the average return per bet can vary with only two bets. ‖ ‖ step 5 ⋮ Acknowledge that statement C is true due to the law of large numbers, which states that as the number of trials increases, the average of the results should be close to the expected value. ‖ ∻1 Answer∻ ***A, C*** ∻Key Concept∻ ⚹Expected Value and Law of Large Numbers⚹ ∻Explanation∻ ⚹The expected value is a weighted average of all possible outcomes, and the law of large numbers states that as the number of trials increases, the sample average will approach the expected value.⚹◊What is the formula to calculate the expected return for placing multiple bets in this sports betting⍭ Generate me a similar question◊

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