A group of files in a medical clinic classifies the patients by gender and by type of diabetes

(type 1 or type 2). The groupings may be shown as follows. The table gives the number in each classification.

Type of Diabetes Gender 1 2 Male 30 15 Female 35 20

a. Display the information on this 2 2 table as a Venn diagram using “type 1” and “male” as the two events displayed as circles. Explain how the Venn diagram and the given 2 2 table display the same information.

If one file is selected at random, find the probability of the following:

b. The selected individual is female.

c. The selected individual has type 2 diabetes.