Question

A hat contains four balls. The balls are numbered 2, 4, 4, and 7. One ball is randomly selected and

not replaced, and then a second ball is selected. The numbers on the two balls are added together.
A fair decision is to be made about which of three sizes of ice cream cone will be ordered, using the
sum of the numbers on the balls. The sizes are small, medium and large.
Which description accurately explains how a fair decision can be made in this situation?
If the sum is 6, a small cone will be ordered.
If the sum is 8 or 9, a medium cone will be ordered.
If the sum is 11, a large cone will be ordered.
If the sum is 6 or 9, a small cone will be ordered.
If the sum is 8, a medium cone will be ordered.
If the sum is 11, a large cone will be ordered.
O
If the sum is 6, a small cone will be ordered.
If the sum is 8 or 11, a medium cone will be ordered
If the sum is 9, a large cone will be ordered.
If the sum is 6 or 8, a small cone will be ordered.
If the sum is 9, a medium cone will be ordered.
If the sum is 11, a large cone will be ordered

Answer 1

• If the sum is 6, a small cone will be ordered.
• If the sum is 8 or 9, a medium cone will be ordered.
• If the sum is 11, a large cone will be ordered.

Explanation:

The table below shows the possible outcomes from drawing two balls. We see the relative frequencies to be ...

6: 4

8: 2

9: 2

11: 4

To make a fair decision, we want the relative frequencies of the decision possibilities to be the same. If we combine sums 8 and 9 to one category (medium cone, for example), then 6, (8 or 9), and 11 will all have the same relative frequency: 4.

The appropriate "fair decision" choice is ...

6: small cone

8 or 9: medium cone

11: large cone