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?

a) 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.
b) 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.
c) 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.
d) 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.

Answer 1

a) 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:

The sum table can be represented as :

1 2 4 7 8

1 X 3 5 8 9

2 3 X 6 9 10

4 5 6 X 11 12

7 8 9 11 X 15

8 9 10 12 15 X

The Probability sum is a factor of 30 = P(sum is 3, 5, 6, 10, 15)

=
`(2)/(20) +(2)/(20)+(2)/(20)+(2)/(20)+(2)/(20)`

=
`(10)/(20)`

=
`(1)/(2)`

The Probability sum less than 10 = P(sum is 3,5,8,9,6)

=
`(2+2+2+4+2)/(20)`

=
`(3)/(5)`

The probability sum is even = P( sum is 6,8,10, 12)

=
`(2+2+2+2)/(20)`

=
`(8)/(20)`

=
`(2)/(5)`

The probability sum is a multiple of 3 = P( sum is 3,6,9,12,15)

=
`(12)/(20)`

=
`(3)/(5)`

since the probability that is the sum of the ball is a factor of 30 is
`(1)/(2)` , Thus, the probability that the sum is not a factor of 30 will also be
`(1)/(2)` . Thus; the description that accurately explains how a fair decision can be made in this situation is option A.

a) 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.