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Chapter 6: Problem 3

An experiment requires a sequence of three steps. The first step can result in two possible outcomes, the second in three possible outcomes, and the third in five possible outcomes. What is the total number of outcomes possible?

Short Answer

Expert verified
The total number of possible outcomes for the entire sequence of three steps is 30. We can find this by using the counting principle and multiplying the number of outcomes for each step together: \(2 * 3 * 5 = 30\).

Step by step solution

01

Identify the outcomes of each step

In this experiment, there are different numbers of outcomes for each step: - First step: 2 possible outcomes - Second step: 3 possible outcomes - Third step: 5 possible outcomes
02

Apply the counting principle

Using the counting principle, we can find the total number of possible outcomes for the entire sequence by multiplying the number of outcomes for each step together: Total number of outcomes = (Number of outcomes for step 1) * (Number of outcomes for step 2) * (Number of outcomes for step 3)
03

Calculate the total number of outcomes

Now, we plug the numbers of outcomes for each step from Step 1 into the formula from Step 2: Total number of outcomes = (2 outcomes) * (3 outcomes) * (5 outcomes) Total number of outcomes = 30 The total number of possible outcomes for the entire sequence of three steps is 30.

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