Question

1. A surgical procedure requires choosing among four alternative methodologies. The first can result in five possible outcomes, the second can result in three possible outcomes, and the remaining methodologies can each result in two possible outcomes. What is the total number of outcomes possible?

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

3. For the given decision algorithm, find how many outcomes are possible. HINT [See Example 1.]

Step 1:		Step 2:
Alternative 1: 1 outcome		Alternative 1: 2 outcomes
Alternative 2: 2 outcomes		Alternative 2: 5 outcomes
		Alternative 3: 1 outcome

Answer 1

1) Number of Total Outcomes = Number of first possible outcomes + Number of second possible outcomes + Number of outcomes for remaining methodologies = 5 + 3 + 2 + 2 + 2 = 14 outcomes

2) Total Number of outcomes = First Step outcomes * Second step outcomes * Third step outcomes = 3 * 4 * 6 = 72 outcomes

3) Alternative 1 = 1 * 2 = 2

Alternative 2 = 2 * 5 = 10

Alternative 3 = 3

Total outcomes = 2 + 10 + 3 = 15

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