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Chapter 3: Q. 3.26 (page 99)

Suppose that5percent of men and0.25 percent of women are color blind. A color-blind person is chosen at random. What is the probability of this person being male? Assume that there are an equal number of males and females. What if the population consisted of twice as many males as females?

Short Answer

Expert verified

Determine the proportions of men and women in the defined populations. Apply the Bayes formula:
[2ex]P1=2021[lex]P2=4041

Step by step solution

01

Step1:Introduction

Considered events:

C - A person chosen at random is colorblind.

M -A male was chosen at random.

F - A female was chosen at random.

Given probabilities:

P(C鈭�M)=5%P(C鈭�F)=0.25%

P(M)=P(F)

II)P(M)=2脳P(F)

02

Find men and women make up the whole population

Use the Bayes formula (obtained by breaking C into C M and C F )

P(M鈭�C)=P(C鈭�M)脳P(M)P(C鈭�M)P(M)+P(C鈭�F)P(F)

The majority of the population is made up of men and women.

P(M)=P(F)鈬�P(M)=P(F)=0.5

P(M鈭�C)=0.05脳0.50.05脳0.5+0.0025脳0.5

=2021

03

  Step3: The probability of this person being male 

The majority of the population is made up of men and women.

P(M)=2P(F)鈬�P(M)=23,P(F)=13

P(M鈭�C)=0.05脳230.05脳23+0.0025脳13

=4041

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