AnswersMathematics III AExpected Value

Expected Value Answers

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Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?

Question illustration
T
The odd numbered regions will add one point. The even numbered regions lose one point.
R
Red will add one point. Any other color will lose one point.
A
A number less than or equal to 3 will add one point.A 4 will lose two points.
O
Odds will add a point value equal to the number on the space.Evens will lose a point value equal to the number on the space.
2
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A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expected value for a ticket?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Penny Points

E
E(penny) = –0.33 and E(nickel) = 0.33, so she should play with the nickels.
E
E(penny) = 0.5 and E(nickel) = 1.5, so she should play with the nickels.
E
E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.
E
E(penny) = 2.38 and E(nickel) = 2, so she should play with the pennies.
4

Two black chips and three red chips are put into a bag. Two points are awarded for each black chip drawn, and one point is lost for each red chip drawn. What is the expected value for each round if there are two draws per round and the chips are replaced after each draw?

–
–0.08
–
–0.04
0
0.2
0
0.4
5

Which statement below correctly depicts the expected value of a fair game?

E
E(X) = 0
E
E(X) = 1
E
E(X) > 0
E
E(X) >1
6

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect $4,500 from the participants. If the chance of rain is 20%, what is the expected value for the tournament?

–
–$800
–
–$200
$
$2,600
$
$3,400
7

Scoring Schemes of Multiple-Choice Tests

Question illustration
s
scheme A
s
scheme B
s
scheme C
s
scheme D
8

Johnny is challenged to a single-player game with an expected value of 1. Which statement below is true?

I
It is a fair game.
I
It is a favorable game.
I
It is unfavorable game.
J
Johnny cannot determine whether the game is fair without knowing the rules.
9

A business has an opportunity to invest $35,000. If the investment is a success, the business earns a profit of $150,000. Otherwise, the investment will result in a total loss of all monies. If the investment has 0.27 chance of success, which equation correctly models the expected value of this investment?

0
0.27(150,000) + 0.73(–35,000) = E(X)
1
150,000 – 0.73(35,000) = E(X)
0
0.27(150,000 – 35,000) = E(X)
0
0.27(115,000) + 0.73(–35,000) = E(X)
10

best

c
company A
c
company B
c
company C
A
All companies have a probability of loss.

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