Problem

If a first experiment has 3 distinct outcomes and a second experiment has 3 distinct outcomes, then the two experiments together have how many distinct outcomes?

Solution

Step 1 :Given that a first experiment has 3 distinct outcomes and a second experiment also has 3 distinct outcomes.

Step 2 :The number of distinct outcomes of two experiments performed together is the product of the number of outcomes of each experiment. This is because for each outcome of the first experiment, there are as many outcomes of the second experiment.

Step 3 :So, if the first experiment has 3 outcomes and the second experiment also has 3 outcomes, then the total number of outcomes when the two experiments are performed together is \(3 \times 3 = 9\).

Step 4 :Final Answer: The two experiments together have \(\boxed{9}\) distinct outcomes.

From Solvely APP
Source: https://solvelyapp.com/problems/L9C1fn5gwx/

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