Question

A spinner has 4 equally sized sectors that are numbered 3, 3, 4 and 6. The spinner is spun twice and the sum of the outcomes is found.

A fair decision is to be made about which one of 4 vacation destinations will be planned, using the sum of the outcomes.

The vacation destination options are New Mexico, Alaska, Puerto Rico and London.

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

If the sum is 6, the vacation destination will be London. If the sum is 8, the vacation destination will be Alaska. If the sum is 9, the vacation destination will be New Mexico. If the sum is 7, 10 or 12, the vacation destination will be Puerto Rico.

If the sum is 6, the vacation destination will be London. If the sum is 7, the vacation destination will be Alaska. If the sum is 10, the vacation destination will be New Mexico. If the sum is 8, 9 or 12, the vacation destination will be Puerto Rico.

If the sum is 6, the vacation destination will be London. If the sum is 7, the vacation destination will be Alaska. If the sum is 9, the vacation destination will be New Mexico. If the sum is 8, 10 or 12, the vacation destination will be Puerto Rico.

If the sum is 10, the vacation destination will be London. If the sum is 7, the vacation destination will be Alaska. If the sum is 9, the vacation destination will be New Mexico. If the sum is 6, 8 or 12, the vacation destination will be Puerto Rico.

Answer 1

If the sum is 6, the vacation destination will be London.

If the sum is 7, the vacation destination will be Alaska.

If the sum is 9, the vacation destination will be New Mexico.

If the sum is 8, 10 or 12, the vacation destination will be Puerto Rico.

Explanation:

Create a sample space for the 2 spins (see attached).

From the sample space, the probabilities are:

• P(sum is 6) = 4/16
• P(sum is 7) = 4/16
• P(sum is 8) = 1/16
• P(sum is 9) = 4/16
• P(sum is 10) = 2/16
• P(sum is 12) = 1/16

Therefore, to make a fair decision:

As the sum of 6, 7 and 9 each have equal probabilities (4/16), they should each be attritbuted to one destination.

As the sum of 8, 10 and 12 combined equal the same probability as the sum of 6, 7, and 9 individually, the sum of 8, 10 and 12 should be assigned to one destination combined.

Solution

If the sum is 6, the vacation destination will be London.

If the sum is 7, the vacation destination will be Alaska.

If the sum is 9, the vacation destination will be New Mexico.

If the sum is 8, 10 or 12, the vacation destination will be Puerto Rico.