Question

If you run both events together, how many outcomes are possible? Does this offer a fair, unbiased way to pick a vice president from 30 candidates? Note that for this question, you will use counting rule 2: Rule 2: If K1 outcomes can occur during a trial of one experiment, and K2 outcomes can occur during a trial of another experiment, then K1 * K2 different sequences can result.

Answer 1

Let's break down the steps in this problem-solving process.

1. Firstly, we have two events. Both of these events have 30 different possible outcomes or candidates.

2. According to Rule 2 of counting in probability, if one event can occur in K1 ways and a second event can occur in K2 ways, the total number of ways or outcomes both events can occur is given by the multiplication of these outcomes. This is because each possibility from the first event can be paired with each possibility from the second event.

3. Let's apply Rule 2 to our events. For our first event, there are 30 possibilities (K1 = 30) and for our second event, there are also 30 possibilities (K2 = 30).

4. If we multiply these possibilities together, we get the total number of possible sequences for both events to occur. So, K1 * K2 = 30 * 30 = 900.

5. Now let's address the second part of your question: does this offer a fair, unbiased way to select a vice president from 30 candidates?

6. The fairness of the selection process depends on whether each candidate has an equal chance of being selected. In this case, if each candidate is equally likely to be selected in both events, then yes, we can say that the method of selection is both fair and unbiased.

So, for both events together, we have 900 different possible sequences or outcomes. With each individual candidate having an equal chance of being selected, this indeed offers a fair and unbiased way to select a vice president from the group of 30 candidates.