USING PROBABILITY TO MAKE FAIR DECISIONS 1st Period

Brett and Sofia are playing with playing cards. They decide to shuffle a deck of playing cards. After a shuffle they choose a single card. If that card is of an Ace or a King they win 2 points. If that card is of a Jack or a Queen they win 3 points. If that card is of any other number, they lose 1 point. Is this game fair?

• Fair

• Not fair

Eliza and Alisha are the two baseball captains. They roll a die and decide that if the die lands with an even number, Eliza’s team will bat first. Otherwise Alisha’s team will bat first. Is this method fair?

• Fair

• Not fair

Smith and his cousins are rolling dice. They decide that if they roll a 1 or 2 then they will win 3 points. If the number is 3 or 4 then they win 4 points. If they roll a 5 or 6 they win 5 points. Is this game fair?

• Fair

• Not fair

Maria and Mary are playing with dice. They roll one die. If the die lands on the number 2 then they win 7 candies. If the die lands on the number 5 then they win one candy. If the die lands on any other number, they lose 2 candies. Is this game fair?

• Fair

• Not fair

Given the probability model in the table below, what is the expected value of the random variable?

X: 500, 200, 50;

P(X): 0.3, 0.3, 0.4

• 140

• 14

• 7.5

• 230

Suppose there’s a game where the player rolls a die, and either wins or loses money according to these rules.

Dice Roll:   1,  2,  3      Outcome:  Lose $5.00
Dice Roll:   4  or 5       Outcome:  Lose $1.00
Dice Roll:  6                 Outcome:  Win $10.00

Is this a fair game, and why?

• Fair, Expected Value = $1.67

• Not fair, Expected Vlaue = -$1.67

• Fair, Expected Value = 0

• Not Fair, Expected Value = 0

In a game you flip a coin twice, and record the number of heads that occur. You get 10 points for 2 heads, zero points for 1 head, and 5 points for no heads. What is the expected value for the number of points you’ll win per turn?

• -3.75

• 1

• 0

• 3.75

1. A mysterious card-playing squirrel (pictured) offers you the opportunity to join in his game. The rules are:

· To play you must pay him $5.

· If you pick a ten or a face card from a shuffled pack, you win $10.

Is this game fair? What is the expected value?

• Yes; The expected value is zero

• No; The expected value is -$100

• Yes; The expected value is -$1.92

• No; The expected value is -$1.92

The ratio of tails after 3,000 flips of a coin is .45 -- does this mean experimental probability is right and hypothetical probability is wrong? What could I do to test this hypothesis further?

• Yes, hypothetical probability is wrong -- it only predicts what could happen but doesn't need to have anything to do with reality

• No, hypothetical probability is right -- more experiments need to be done according to the Law of Large Numbers

• Yes, hypothetical probability is wrong in this particular case but in others it might be right (it depends)

• No, hypothetical probability is right, someone recorded wrong information in the experiments!

A local club plans to invest $10,000 to host a baseball game. They expect to sell tickets worth $15,000. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. If the weather forecast for the day of game is 20% possibility of rain, is this a good investment?

• Yes, it is a good investment, the expected return is $1,000

• Yes, it is a good investment, the expected return is $2,000

• No, it is not a good investment, the expected return is -$1,000

• No, it is not a good investment unless there is 0% chance of rain