1. A hat contains 5 balls. The balls are numbered 1, 3, 4, 5, and 7. One ball is randomly selected and not replaced, and then a second ball is selected. The numbers on the 2 balls are added together.

A fair decision is to be made about which one of two candy bars to purchase, using the sum of the numbers on the balls.

The candy bar options are Choco Delight or Go Nuts.

Which description accurately explains how a fair decision can be made in this situation?

If the sum of the balls is less than 9, purchase Choco Delight. If the sum is 9 or greater, purchase Go Nuts.

If the sum of the balls is even, purchase Choco Delight. If the sum is odd, purchase Go Nuts.

If the sum of the balls is a factor of 40, purchase Choco Delight. If the sum is not a factor of 40, purchase Go Nuts.

If the sum is a multiple of 4, purchase Choco Delight. If the sum is not a multiple of 4, purchase Go Nuts.

2.

A spinner has four equally sized sectors that are numbered 1, 2, 6, and 6. The spinner is spun twice and the product of the outcomes is found.

A fair decision is to be made about which one of four flowers will be planted.

The flower options are peonies, roses, asters or petunias.

Which description accurately explains how a fair decision can be made in this situation?

If the product of the spins is 6, peonies will be planted. If the product is 12, roses will be planted. If the product is 36, asters will be planted. If the product is 1, 2 or 4, petunias will be planted.

If the product of the spins is 6, peonies will be planted. If the product is 12, roses will be planted. If the product is 1 or 36, asters will be planted. If the product is 2 or 4, petunias will be planted.

If the product of the spins is 4, peonies will be planted. If the product is 12, roses will be planted. If the product is 36, asters will be planted. If the product is 1, 2 or 6, petunias will be planted.

If the product of the spins is 6, peonies will be planted. If the product is 4, roses will be planted. If the product is 36, asters will be planted. If the product is 1, 2 or 12, petunias will be planted.

TheFA May 28, 2019

#1**+1 **

1. A hat contains 5 balls. The balls are numbered 1, 3, 4, 5, and 7. One ball is randomly selected and not replaced, and then a second ball is selected. The numbers on the 2 balls are added together.

A fair decision is to be made about which one of two candy bars to purchase, using the sum of the numbers on the balls.

The candy bar options are Choco Delight or Go Nuts.

Which description accurately explains how a fair decision can be made in this situation?

If the sum of the balls is less than 9, purchase Choco Delight. If the sum is 9 or greater, purchase Go Nuts.

If the sum of the balls is even, purchase Choco Delight. If the sum is odd, purchase Go Nuts.

If the sum of the balls is a factor of 40, purchase Choco Delight. If the sum is not a factor of 40, purchase Go Nuts.

If the sum is a multiple of 4, purchase Choco Delight. If the sum is not a multiple of 4, purchase Go Nuts.

1 3 4 5 7

Possible outcomes

(1, 3) (1, 5) (3,4) (3,7) (4,7)

(3,1) (5, 1) (4,3) (7,3) (7, 4)

(1, 4) (1, 7) (3,5) (4,5) (5, 7)

(4, 1) (7,1) (5, 3) (5,4) (7, 5)

Let's look at each situation

P(sum< 9) = 12/20 P (sum 9 or greater) = 8/20 not fair

P(even sum) = 12/20 P(odd sum) = 8/20 not fair

P(sum is a factor of 40) = 10/20 P (sum is not not a factor of 40) = 10/20

P(sum is a multiple of 4) = 8/20 P (sum is not a multiple of 4) = 12/20

The third answer provides a fair decision

CPhill May 28, 2019

#3**+1 **

A spinner has four equally sized sectors that are numbered 1, 2, 6, and 6. The spinner is spun twice and the product of the outcomes is found.

A fair decision is to be made about which one of four flowers will be planted.

The flower options are peonies, roses, asters or petunias.

Which description accurately explains how a fair decision can be made in this situation?

Let's look at a table of possible outcomes

1 2 6 6

1 1 2 6 6

2 2 4 12 12

6 6 12 36 36

6 6 12 36 36

Now ....let's consider each situation

If the product of the spins is 6, peonies will be planted. If the product is 12, roses will be planted. If the product is 36, asters will be planted. If the product is 1, 2 or 4, petunias will be planted.

P(prod = 6) =1/4 P(prod = 12) = 1/4 P( prod = 36) = 1/4 P(prod = 1, 2 or 4) = 1/4

We can stop here.....this provides a fair division....each flower has an equal chance of being planted

CPhill May 28, 2019