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In probability and statistics, experimental outcomes are all the possible results that can occur from an experiment. For this blood analysis, we are dealing with two procedures, each having a set number of steps. Procedure 1 can take 1 or 2 steps, while Procedure 2 can take 1, 2, or 3 steps.

To find the experimental outcomes, we need to consider every possible combination of steps from both procedures. This involves pairing each outcome from Procedure 1 with each outcome from Procedure 2. The combinations are as follows:

• (1,1)
• (1,2)
• (1,3)
• (2,1)
• (2,2)
• (2,3)

Each pair represents one way the procedures might be completed, showing the number of steps for Procedure 1 first, followed by the number of steps for Procedure 2. By listing these outcomes, we gain a clear view of all potential experimental scenarios before calculating additional data such as a random variable.

A random variable is a numerical representation of the outcomes in a probability experiment. In the context of this exercise, the random variable refers to the total number of steps taken to complete both procedures. Each outcome will map to a value in the set of possible total steps.

For each pair outcome (a, b), where 'a' is the step count for Procedure 1 and 'b' is for Procedure 2, the total steps are calculated by simple addition:

• (1, 1) results in 1 + 1 = 2 total steps
• (1, 2) results in 1 + 2 = 3 total steps
• (1, 3) results in 1 + 3 = 4 total steps
• (2, 1) results in 2 + 1 = 3 total steps
• (2, 2) results in 2 + 2 = 4 total steps
• (2, 3) results in 2 + 3 = 5 total steps

These computations show different possible values that the random variable can assume: 2, 3, 4, or 5. By understanding random variables, we can transform complex scenarios into quantifiable data points that are easier to analyze statistically.

Combinatorics is a field of mathematics that deals with counting and arranging possibilities. It's essential when considering the range of potential outcomes in a probability experiment, like the one in this blood analysis exercise.

In this scenario, combinatorics help to determine how many distinct ways we can conduct both procedures based on their step requirements. By using combinatorial principles, we take the distinct options for each procedure and combine them consistently. As Procedure 1 has 2 options (1-step or 2-step) and Procedure 2 has 3 options (1-step, 2-step, or 3-step), the total number of experimental outcomes is found by multiplying the number of choices for each procedure:

- Total Outcomes = Number of P1 choices × Number of P2 choices
- Total Outcomes = 2 × 3 = 6

Combinatorics allows us efficiently to account for all potential experimental outcomes, simplifying what might otherwise be a tedious task of listing every possibility manually. This discipline is a backbone in probability theory, helping us systematically explore all possible scenarios.