Free Using probability to make fair decisions Practice Problems • Learn To Be

Amy and Miranda are arguing over who gets to use the car on Saturday night. Amy wants to go to see a play with her friends and Miranda wants to go to the mall with her friends.

Which of the following are fair methods for making a decision?

(Consider a system to be fair when the probabilities of each event are equal.)

Choose all answers that apply:

A
The girls have a scale that is accurate to the nearest hundredth of a gram. They put a sack of potatoes on the scale. If the hundredths digit is even, Miranda gets to use the car. If the hundredths digit is odd, Amy gets to use the car.
B
The girls decide to look up the $75$ th digit of pi - something neither of them has any knowledge of. If the $75$ th digit is even, Miranda gets the car. If it is odd, Amy gets the car.
C
Amy pulls out her graphing calculator. She commands the calculator to generate a random integer from $1$ to $15$ (inclusive). If the number is $7$ or below, Amy gets the car. If the number is $9$ or above, Miranda gets the car. If the number is $8$ , they generate a new number and repeat.
D
Amy throws two pennies into the air. If they are both heads, Amy gets the car. Otherwise, Miranda gets the car.

Using probability to make fair decisions

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