HomeStyle is an online retailer of home accessories for every room in the home.

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1. Let us re-examine the frequency table in question 1 as a summary of observed probabilities.
2. Construct a probability table for the data in question 1. The probabilities reflect the observed relative frequencies of occurrence. The body of the table will show the joint probability of each combination of gender and type of purchase. Include row totals showing the probability of purchase type and the column totals showing the probability of gender. Round probabilities to 2 decimals.
3. Suppose that gender and type of purchase was independent for each possible combination. Construct an idealized probability table that we should have observed if these factors were independent. The row and column totals should remain the same as in a) but the body of the table will change somewhat. Round probabilities to 2 decimals.
4. The table in a) is simply a summary of approximately 1,000 purchases. If HomeStyle were to look at another sample of 1,000 purchases it would get a somewhat different table. Do you think the tables in a) and b) are sufficiently different from each other that you would conclude that the purchasing behavior of females, males and "unknown" are different from each other? For now we are just looking for your opinion. You don't have the knowledge yet to properly say whether they ae different.
5. Comparing large tables with small differences may hide patterns. If you really want to see differences between purchasing patterns of females, males and unknowns, calculate P{Bed&Bath | female}, P{Bed & Bath | male} and P{ Bed&Bath | unknown}. Repeat this for the other categories. Summarize these conditional probabilities in a table. Use 2 decimals.
6. Does knowing the customer's gender give you any insight with respect to what the customer is more or less likely to buy?