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