Suppose that a survey on color blindness yields the followin

Suppose that a survey on color blindness yields the following results:

Sex Color Blind Not Color Blind

Female 7 1492

male 53 1315

If person who was surveyed is selected at random, find the probability that they

a.) are not color blind given taht they are female

b.) are male given that they are color blind

I know this question is not hard. I am an international student so I just want to see other\'s answer to make sure I understand the question correctly.

Solution

Following table shows the row total and column totals:

(a)

Out of 2867 people, 1499 are females. So the probbaility that a randomly selected person is a female will be

P(female) = 1499 /2867

And there are 1492 persons who are not color blind an female so

P(not color blind and female) = 1492 /2867

So the probability that a randomly selected person is not color blind given that they are female will be

P(not color blind | female) = P(not color blind and female) / P(female) = (1492/2867) / (1499/2867) = 1492/1499

(b)

P(color blind) = 60/ 2867

P(male and color blind) = 53/2867

So the probability that are male given that they are color blind will be

P(male | color blind) = P(male and color blind) / P(color blind) = (53/2867) / (60/2867) = 53 / 60