Question

A. The two spinners shown below are being used in a probability experiment.

During each trial of the experiment, the arrows on the spinners are spun once, and the outcome is recorded. For example, an outcome of (2, 1) means that the arrow pointed to 2 on the first spinner and pointed to 1 on the second spinner.

B. What is the theoretical probability that, during each trial of the experiment, the result has at least one 4 on the spinners? Show your work or explain your answer.

Explain why the experimental probability from the results does not agree with the theoretical probability you found in part B.

Answer 1

The theoretical probability of at least one 4 on the spinners is 0.4375

(a) The number of different outcomes

The sections on the spinners are:

Spinner 1 = 4

Spinner 2 = 4

So, the number of different outcomes is:

Outcomes = 4 * 4

Outcomes = 16

Hence, the number of different outcomes is 16

(b) The theoretical probability of at least one 4 on the spinners

The spin results that have at least one 4 are:

Results = {(4,1), (4,2), (4,3), (4,4), (1,4), (2,4), (3,4)}

The count of these results is 7.

So, the theoretical probability of at least one 4 on the spinners is:

P = 7/16

P = 0.4375

Hence, the theoretical probability of at least one 4 on the spinners is 0.4375

(c) Why the theoretical probability and the experimental probability are different?

The theoretical probability and the experimental probability are different because:

• Experimental probabilities are based on the actual experiment
• Theoretical probabilities are based on the logic

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