Question

A hat contains 5 balls. The balls are numbered 1, 2, 4, 7, and 8. 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 restaurants to eat at, using the sum of the numbers on the balls.

The restaurant options are Joe's Place or Taco Towne.

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




If the sum of the balls is less than 10, eat at Joe's Place. If the sum of the balls is 10 or more, eat at Taco Towne.

If the sum of the balls is a factor of 30, eat at Joe's Place. If the sum is not a factor of 30, eat at Taco Towne.

If the sum of the balls is a multiple of 3, eat at Joe's Place. If the sum is not a multiple of 3, eat at Taco Towne.

If the sum of the balls is even, eat at Joe's Place. If the sum of the balls is odd, eat at Taco Towne.

Answer 1

If the sum of the balls is a factor of 30, eat at Joe's Place. If the sum is not a factor of 30, eat at Taco Towne.

Explanation:

By listing out all the probabilities you can get by drawing the balls, the answer is so because you have an equal number of sums that are factors of 30 and sums that are factors of less than 30.

(To have it fair, both criteria need to have the same probability.)

The probabilities you have are

: 1,2

: 1,4

: 1,7

: 1,8

: 2,4

: 2,7

: 2,8

: 4,7

: 4,8

: 7,8