327 L01-(Winter Problem Color vision deficiency, commonly known as colorblindnes

Question

327 L01-(Winter Problem Color vision deficiency, commonly known as colorblindness, is a decreased ability to see color or to distinguish amongst colors. Due to the fact that most genes responsible for colorblindness are found on the X chromosome, males are more likely to be colorblind than females. Suppose, in a particular population, that if a person is male, they have an 8% chance of also being colorblind. If a person is female, they have a 1% chance of also being colorblind. Suppose also that females make up 53% of this particular population. a) Use this information to complete the following contingency table. Not Colorblind Colorblind Row Totals Male Female Column Totals b) A person is randomly selected from this population. What is the probability that they c) A person is randomly selected from this population. What is the probability that they d) Assuming that a randomly-selected person from this population is not colorblind, e) Are the events "male" and "not colorblind" mutually exclusive? Show why/why not are colorblind? are male or colorblind? what is the probability that they are female? using probability

Explanation / Answer

Solution:

Given,

Probability of being colorblind for a male = 0.08

Probability of being colorblind for a female = 0.01

Probability of picking a female = 0.53

probability of picking a male = 1-0.53 = 0.47

probability of picking a male colorblind = 0.47 * 0.08 = 0.037

probability of picking a non colorblind male = 0.92 * 0.47 = 0.432

probability of picking a female colorblind = 0.53 * 0.01 = 0.005

probability of picking a non colorblind female = 0.99 * 0.53 = 0.524

a)

b) probability of selecting color blind = probability of picking male colorblind + probability of picking female color blind

= 0.037 + 0.005 = 0.042

c) probability of male + probability of female colorblind = 0.47 + 0.005 = 0.475

d) probability of picking a female from noncolor blind = probablity of noncolor blind female / total probability of not colorblinds

= 0.529/ 0.961

= 0.55

e) They are not mutually exclusive because there are 0.432 non color blind males.

Colorblind Not colorblind Row Totals Male 0.037 0.432 0.047 Female 0.005 0.529 0.053 Coulm Totals 0.042 0.961 1

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.