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?

​
0.25




​Part B

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

​
0.625


​

​Part C

What is the probability that the selected person has diabetes?

​
0.40


​

​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?

​


are they dependent or not independsent

Answer 1

They are independent.

Reason: P(male and has diabetes) = 40/160 = 0.25.
P(male)·P(has diabetes) = 0.625·0.40 = 0.25, so P(male and diabetes) = P(male)P(diabetes).
Equivalently, P(diabetes | male) = 40/100 = 0.40 = P(diabetes). Thus the events are independent.