## Related questions with answers

For the decision algorithms in this exercise, find how many outcomes are possible.

$\begin{matrix} \text{Step 1:} & \text{Step 2:}\\ \text{Alternative 1: 1 outcome} & \text{Alternative 1: 2 outcomes}\\ \text{Alternative 2: 2 outcomes} & \text{Alternative 2: 2 outcomes}\\ & \text{Alternative 3: 1 outcome}\\ \end{matrix}$

Solution

VerifiedNote: 'alternative' implies addition principle, 'step' implies multiplication principle.

Let's first observe $\textbf{Step 1}$.

Alternative 1 has 1 outcome.

Alternative 2 has 2 outcomes.

In total, there are $1+2 = 3$ possible outcomes in Step 1.

Let's now take a look at $\textbf{Step 2}$.

Alternative 1 has 2 outcomes.

Alternative 2 has 2 outcomes.

Alternative 3 has 1 outcome.

In total, there $2+2+1 = 5$ possible outcomes in Step 2.

Finally, we have 3 possible outcomes in Step 1 and 5 possible outcomes in Step 2. Therefore, there are $3\cdot 5 = 15$ possible outcomes in total.

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