Decision-Making with EV Quiz (HSS.MD.A.2)

1) Bag of marbles expected value?

$2.80

$3.60

$4.00

$4.80

EV = (4/10)*6 + (3/10)*4 = 36/10.

Explanation

EV = (4/10)*6 + (3/10)*4 = 36/10.

2) Insurance deductible choice?

Option 2

Option 1

Equal

Cannot determine

Option 1 EV = 100 < 200.

Explanation

Option 1 EV = 100 < 200.

3) Game expected value?

−0.20

0

+0.70

0.80

EV = 3.2 − 1.5 −1 = 0.7.

Explanation

EV = 3.2 − 1.5 −1 = 0.7.

4) Spinner new expected net gain?

$0.40

$0.80

$1.00

$2.00

EV payout = 27/5 = 5.4 → net = +0.4.

Explanation

EV payout = 27/5 = 5.4 → net = +0.4.

5) Spinner expected net gain?

−1

0

−0.60

+0.40

4.4 − 5 = −0.6.

Explanation

4.4 − 5 = −0.6.

6) Spinner expected payout?

$3.60

$5.00

$6.40

$4.40

EV = 22/5 = 4.4.

Explanation

EV = 22/5 = 4.4.

7) Mystery bag expected net value?

−1

−0.30

+1.50

0.50

EV = 6.5; net = +1.5.

Explanation

EV = 6.5; net = +1.5.

8) Phone plan lower expected cost?

Plan B

Plan A

They are equal

Cannot determine

Plan A = 40; Plan B = 50.

Explanation

Plan A = 40; Plan B = 50.

9) Investment X expected return?

$50

$65

$80

$100

EV = 60 + 25 − 20 = 65.

Explanation

EV = 60 + 25 − 20 = 65.

10) Card draw expected net value?

+0.46

−1

0

0.12

Expected prize ≈ 1.46; net ≈ 0.46.

Explanation

Expected prize ≈ 1.46; net ≈ 0.46.

11) What is the expected payout (before subtracting the $3 cost) of one spin?

$2.00

$2.75

$3.00

$3.25

There are 8 equal sectors. Expected payout = (3/8)*2 + (2/8)*5 + (1/8)*10 + (2/8)*0 = 26/8 = $3.25.

Explanation

There are 8 equal sectors. Expected payout = (3/8)*2 + (2/8)*5 + (1/8)*10 + (2/8)*0 = 26/8 = $3.25.

12) Warranty good deal?

Yes; EV savings > 30

Yes; expected repair cost is 35

No; EV savings < 30

No; EV savings = 0

Expected repair cost = 30, same as warranty.

Explanation

Expected repair cost = 30, same as warranty.

13) Which game has higher expected net value?

Game A

Game B

They are equal

Neither

Game A net = +1; Game B net ≈ −0.67.

Explanation

Game A net = +1; Game B net ≈ −0.67.

14) Charity raffle expected net value?

−$10

−$5

−$3

−$4

Expected prize = 6. Net = 6 − 10 = −4.

Explanation

Expected prize = 6. Net = 6 − 10 = −4.

15) Insurance break-even premium?

$50

$100

$200

$5000

0.02 * 5000 = 100.

Explanation

0.02 * 5000 = 100.

16) Lottery ticket expected net value?

−$1.29

−$0.50

−$1.60

$0.71

Expected prize = 0.4. Net = 0.4 − 2 = −1.6.

Explanation

Expected prize = 0.4. Net = 0.4 − 2 = −1.6.

17) A fair six-sided die... expected value?

$1.50

$3.50

$3.00

$4.00

EV = (1/6)*12 + (2/6)*3 = 18/6 = 3.

Explanation

EV = (1/6)*12 + (2/6)*3 = 18/6 = 3.

18) If a player spins 100 times, what is the best estimate of the total net gain?

$25

$0

$50

−$25

Expected gain per spin = $0.25. For 100 spins: $25.

Explanation

Expected gain per spin = $0.25. For 100 spins: $25.

19) Based on expected value, is the game favorable to the player?

Yes, expected value is positive

No, expected value is negative

It’s fair (expected value is zero)

Cannot be determined

Expected net gain is +$0.25.

Explanation

Expected net gain is +$0.25.

20) What is the expected net gain (payout minus $3 cost) per spin?

−$0.25

$0.50

$1.00

$0.25

Expected payout = $3.25. Net gain = 3.25 − 3.00 = $0.25.

Explanation

Expected payout = $3.25. Net gain = 3.25 − 3.00 = $0.25.

Using Expected Value in Decision-Making Quiz

1) Bag of marbles expected value?

2)

What first name or nickname would you like us to use?

2) Insurance deductible choice?

3) Game expected value?

4) Spinner new expected net gain?

5) Spinner expected net gain?

6) Spinner expected payout?

7) Mystery bag expected net value?

8) Phone plan lower expected cost?

9) Investment X expected return?

10) Card draw expected net value?

11) What is the expected payout (before subtracting the $3 cost) of one spin?

12) Warranty good deal?

13) Which game has higher expected net value?

14) Charity raffle expected net value?

15) Insurance break-even premium?

16) Lottery ticket expected net value?

17) A fair six-sided die... expected value?

18) If a player spins 100 times, what is the best estimate of the total net gain?

19) Based on expected value, is the game favorable to the player?

20) What is the expected net gain (payout minus $3 cost) per spin?