Question

In: Statistics and Probability

In a survey of 177 people, the following data were obtained relating gender to color-blindness: Color-Blind...

In a survey of 177 people, the following data were obtained relating gender to color-blindness:

Color-Blind (C) Not Color - Blind Total
Male (M) 92 36 128
Female (F) 33 16 49
Total 125 52 177


A person is randomly selected. What is the probability that the person is:
a) Male?   
b) Male and Color-blind?  
c) Male given that the person is Color-blind?  
d) Color-blind given that the person is Male?  
e) Female given that the person is not Color-blind?  
f) Are the events Male and Color blind independent?  Enter yes or no.

Solutions

Expert Solution

Total number of people = 177

a)

Number of male = 128

Probability that the person is Male = (Number of male Total number of people) = (128 177) = 0.7232

Answer: 0.7232

b)

Number of Male and Color-blind = 92

Probability that the person is Male and Color-blind = (Number of Male and Color-blind Total number of people)

Probability that the person is Male and Color-blind = (92 177) = 0.5198

Answer: 0.5198

c)

Number of Male and Color-blind = 92

Number of Color-blind = 125

Probability that the person is Male given that the person is Color-blind = (Number of Male and Color-blind   Number of Color-blind)

Probability that the person is Male given that the person is Color-blind = (92 125) = 0.736

Answer: 0.736

d)

Number of Male and Color-blind = 92

Number of Male = 128

Probability that the person is Color-blind given that the person is Male = (Number of Male and Color-blind   Number of Male)

Probability that the person is Color-blind given that the person is Male = (92 128) = 0.7187

Answer: 0.7187

e)

Number of Female and not Color-blind = 16

Number of Not Color-blind = 52

Probability that the person is Female given that the person is not Color-blind = (Number of Female and not Color-blind Number of Not Color-blind )

Probability that the person is Female given that the person is not Color-blind = (16 52) = 0.3077

Answer: 0.3077

f)

If the events Male and Color blind are independent then probability that the person is Male and Color-blind will be equal to the product of probability that the person is Male and probability that the person is Color-blind

We write the above statement in equation form for understanding

If probability that the person is Male and Color-blind = (probability that the person is Male probability that the person is Color-blind) then events Male and Color blind are independent

we know the values of probability from above question except probability that the person is Color-blind

probability that the person is Color-blind = (Number of Color-blind Total number of people) =(125 177) =0.7062

(probability that the person is Male probability that the person is Color-blind) = 0.7232 0.7062 = 0.5107

0.5198 0.5107

So, probability that the person is Male and Color-blind (probability that the person is Male probability that the person is Color-blind)

Therefore, events Male and Color blind are not independent

Answer : no.

orchestra answered 2 years ago
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