Question

Math

Posted 2 months ago

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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.
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Answer from Sia

Posted 2 months ago

Solution by Steps

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.

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