Question

A box contains coins, number cubes labelled 1 to 6, and a spinner with 4 congruent sectors. Which 2 items from the box would you use to simulate a situation with 8 equally likely outcomes?
A) A number cube and a spinner
B) A coin and a number cube
C) Two number cubes
D) A coin and a spinner

Answer 1

Using the Fundamental Counting Theorem, it is found that a simulation with 8 equally likely outcomes would be generated from:

D) A coin and a spinner.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

- The coin has 2 outcomes, hence [tex]n_1 = 2[/tex].

- The spinner has 4 outcomes, hence [tex]n_2 = 4[/tex].

The total number of equally likely outcomes is given by:

N = 2 x 4 = 8.

Hence option D is correct.

More can be learned about the Fundamental Counting Theorem at