Question

A study of
160
160 people recorded their gender and whether they have ​diabetes.
The results of the study are shown in the table below.
​ Has diabetes​ Does not have diabetes​
Male​ ​
40
40 ​
60
60
​Female ​
24
24 ​
36
36
A person is to be selected at random out of the
160
160 people in the study.


​Part A

What is the probability that the selected person is a male and has ​​diabetes?

​




​Part B

What is the probability that the person selected is a male?

​


​

​Part C

What is the probability that the selected person has diabetes?

​


​

​Part D

Based on your answers to Parts A, B, and C, are the events “selected ​person is a male” and “selected person has diabetes” independent or ​not?

Answer 1

Part A
P(male and has diabetes) = 40/160 = 1/4 = 0.25

Part B
P(male) = 100/160 = 5/8 = 0.625

Part C
P(has diabetes) = (40+24)/160 = 64/160 = 2/5 = 0.40

Part D
P(male)·P(has diabetes) = 0.625·0.40 = 0.25 = P(male and has diabetes).
Thus the events "male" and "has diabetes" are independent (also P(has diabetes | male)=40/100=0.40 = P(has diabetes)).