Suppose we have a new population and we are interested in two features named X1, which can take any non-negative integer value, and X2, which takes the values “A”, “B”, or “C” for 30%, 30%, and 40% of the population, respectively. Answer the following questions.

1. Suppose that among the subpopulation of elements with X2 = “A”, the proportion of elements with X1 = 5 is 0.75. What is the proportion of elements in the entire population with X1 = 5 and X2 = “A”?

2. Suppose that in the entire population, the proportion of elements with X1 = 5 and X2 = “B” is 0.18. In the subpopulation of elements wth X2 = “B”, what proportion have X1 = 5?

3. Given the above information, also suppose that among the subpopulation of elements with X2 = “C”, the proportion of elements with X1 = 5 is 0.1. What is the proportion of elements in the entire population with X1 = 5?

4. Given the above information, what proportion of the elements with X1 = 5 have X2 = “C”?

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