Question

A spinner has 4 equally sized sectors that are numbered 1, 2, 2 and 6. The spinner is spun twice and the product of the outcomes is found.
A fair decision is to be made about which one of 4 different paint colors will be used to re-paint a room, using the product of the outcomes.

The color options are pale lilac, mellow sage, seafoam blue and totally taupe.

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

A) If the product of the spins is 2, pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 12, seafoam blue will be used. If the product is 1, 6 or 14, totally taupe will be used.

B) If the product of the spins is 12, pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 14, seafoam blue will be used. If the product is 1, 2 or 6, totally taupe will be used.

C) If the product of the spins is 2, pale lilac will be used. If the product is 1, mellow sage will be used. If the product is 12, seafoam blue will be used. If the product is 4, 6 or 14, totally taupe will be used.

D) If the product of the spins is 2, pale lilac will be used. If the product is 6, mellow sage will be used. If the product is 12, seafoam blue will be used. If the product is 1, 4 or 14, totally taupe will be used.

Answer 1

Answer:

A.

Step-by-step explanation:

Answer 2

First thing, there is a typo in all your answers: there is no way you can get 14 as a product of the numbers of the spinner's sectors, but rather 36.

After this premise, the correct answer is A) If the product of the spins is 2, pale lilac will be used. If the product is 4, mellow sage will be used. If the product is 12, seafoam blue will be used. If the product is 1, 6 or 36, totally taupe will be used.

Explanation:

You have a spinner with 4 sectors that is spinned twice. Therefore, the possible outcomes are 4 × 4 = 16 pairs of numbers:
(1, 1) (1, 2) (1, 2) (1, 6)
(2, 1) (2, 2) (2, 2) (2, 6)
(2, 1) (2, 2) (2, 2) (2, 6)
(6, 1) (6, 2) (6, 2) (6, 6)

The possible products are then,
1    2    2    6
2    4    4  12
2    4    4  12
6  12  12  36

Hence, we have:
1 possible product of 1;
4 possible products of 2;
4 possible products of 4;
2 possible product of 6;
4 possible products of 12;
1 possible product of 36.

Since the paint colors are 4, to make a fair decision, each color should be matched with 16 ÷ 4 = 4 total possible outcomes: the products 2, 4 and 12 each have 4 possible outcomes, the products 1, 6 and 36 together have 4 possible outcomes.

Therefore, a fair decision is taken if we match:
product 2 - color 1
product 4 - color 2
product 12 - color 3
products 1, 6 and 36 - color 4.

Hence, the only correct option is A)