Binomial Probability, Expected Value AMDM

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

• $12.50
• $5
• $7.50
• $10

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Eva flips a coin. If she gets heads, she wins $4. If she gets tails, she loses $3. What is her expected value of a coin flip?

• $1

• $0.50

• -$0.50

• $0

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Suppose you buy a ticket for $6 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. How much money do you take home (after paying for it)?

• $800

• -$6.50

• -$6

• -$5.20

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

CCSS.HSS.MD.A.2

CCSS.HSS.MD.B.5

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. Do you expect to win or lose (on average)? How much?

• lose an average of $5.50

• lose an average of $1.50

• win an average of $2.00

• lose an average of $10.00

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

If the expected value is negative, are you expected to win?

• yes
• no

Answer explanation

If the result is negative you will expect to lose money.

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Eva flips a coin. If she gets heads, she wins $4. If she gets tails, she loses $3. What is her expected value of a coin flip?

• $1

• $0.50

• -$0.50

• $0

Answer explanation

P(Heads) x $4 + P(Tails) x $3

0.5 x 4 - 0.5 x 3

$2 - $1.5 = $0.50

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Now we know Courtneys expected value is $0.50, if she played the game 20 times how much do you expect her to win?

• $20

• $0.50

• $10

Answer explanation

$0.50 x 20 = $10

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

You roll a standard die. You win $12 if you roll a six, $6 if you roll a one, and $0 if you roll anything else. What is the expected value of a single roll?

• $3

• $18

• $9

• $2

Answer explanation

P(6) x $12 + P(1) x $6 - P(2 or 3 or 4 or 5) x $0

1/6 x $12 + 1/6 x $6 - 4/6 x $0

$2 + $1 = $3

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Would you play this game?

• Yes, make me rich

• No, I would have nothing left

Answer explanation

If we played this game then we would expect to win $3 each time so we would definitely play. There is also no chance of losing money.

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses 400 baht. A roll of a blue pays 500 baht. A roll of a green pays 200 baht. Would you play the game? Why or why not?

• No, you expect to lose 50 Baht

• Yes, you expect to win 50 Baht

Answer explanation

P(Blue) x 500 + P(Green) x 200 - P(Red) x 400

1/6 x 500 + 1/3 x 200 - 1/2 x 400

250/3 + 200/3 - 200 = -50 baht

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5