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# an experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. how many experimental outcomes exist for the entire experiment?

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## An experiment has three steps with three outcomes possible f

Find step-by-step Statistics solutions and your answer to the following textbook question: An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?.

### Question

An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?

### Explanation

Verified

\textbf{Fundamental counting principle}

Fundamental counting principle: If the first event could occur in

m

m ways and the second event could occur in

n

n ways, then the number of ways that the two events could occur in sequence is

m\cdot n m⋅n.

The experiment consists of three steps, where there are 3 possible outcomes for the first step, 2 possible outcomes for the second step, and 4 possible outcomes for the third step.

First step: 3 ways Second step: 2 ways

Third step: 4 outcomes

Use the fundamental counting principle:

3\cdot 2\cdot 4=6\cdot 4=24

3⋅2⋅4=6⋅4=24

Thus there exist 24 experimental outcomes for the entire experiment.

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## 1. An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second

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An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?

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James 1 year ago

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