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Question: You have two objects. If you add one more object, how many more permutations will there be?In a sample of millionaires, you want to calculate the probability of a millionaire being a high school dropout who has also earned their own money (rather than inherited it). According to Bayes theorem, and given the following variables, how do you find the numerator to determine this conditional probability? A: the percentage of millionaires who were high school dropouts B: the percentage of millionaires who earned their own money C: the percentage of millionaires who were high school dropouts and earned their own money

First, let's address the permutations question: When you have two objects, there are 2! (factorial) permutations, which is equal to 2*1 = 2. When you add one more object, you will have a total of three objects and thus 3! permutations, which is equal to 3*2*1 = 6. Therefore, there will be 4 more permutations when you add one more object (6 - 2 = 4). Now, let's address the Bayes theorem question: Bayes theorem can be expressed as P(A|B) = P(B|A) * P(A) / P(B). In this case, we are trying to find the probability of a millionaire being a high school dropout (A) who earned their own money (B). Therefore, we want to determine the numerator in P(A|B) = P(A and B) / P(B). To find the numerator, which is P(A and B), we need to use given variable C. Variable C represents the percentage of millionaires who are both high school dropouts and earned their own money. So, the numerator is the value of variable C.

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