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Problem #1: Research shows that Mediterranean Diet is effective in reducing the risk of having colon cancer. To determine if this is true, a random sample of patients with colon cancer and a control group of patients admitted to the hospital for other reasons was obtained, and further classified according to their consumption of olive oil. The data are summarized in the table below: Olive Oil Consumption Total Low Medium High With Colon Cancer 398 397 430 1225 Without Colon Cancer 400 425 320 1145 Total 798 822 750 2370 Suppose a patient in this group is selected. a. What is the probability that the patient selected has colon cancer? b. What is the probability that the patient selected consumes high amount of olive oil and does not have colon cancer? c. If the patient selected do not have colon cancer, what is the probability that the patient consumes high amount of olive oil? d. What is the probability that the patient selected either has colon cancer or consumes low amount of olive oil? e. Using probabilities, determine if the events without colon cancer and high olive oil consumption are independent