4. \"Does Eye Color depend on Gender\" Given the followving survey re:Suppose th

Question

4. "Does Eye Color depend on Gender" Given the followving survey re:Suppose that Blue Brown Green Hazel Male 370 352 98187 Female 359 29010 160 one of these 2026 students is randomly selected. Let F denote the event that the selected individual is a female, and A, B, C and D represents the events that he or she has blue, brown, green and hazel eyes, respectively. (a) Calculate both P(F) and P(C). (b) Find P(FnC). Are the events F and C independent? Why? (c) If the selected individual has green eyes, what is the probability that he or she is a female? (d) If the selected individual is a female, what is the probability that she has greern eyes (e) What is the "conditional distribution" of eye color for females (i.e., P(A F), P(BIF), P(CF), P(D|F), and what is it for males? Compare the two distribu tions

Explanation / Answer

from given table"

a)P(F) =919/2026 =0.4536

P(C) =308/2026 =0.1520

b) P(FnC) =110/2026 =0.0543

as P(FnC) is not equal to P(F)*P(C) ; therefore F and C are not independent

c) P(F|C) =P(FnC)/P(C) =0.3571

d) P(C|F) =P(FnC)/P(F) =0.1197

e)

P(A|F) 359/919 =0.3342

P(B|F) =290/919 =0.3180

P(C|F) =110/919 =0.1789

P(D|F) =160/919 =0.1689

for males

P(A|Fc) 370/1107 =0.3906

P(B|Fc) 352/1107 =0.3156

P(C|Fc) 198/1107 =0.1197

P(D|Fc) 187/1107 =0.1741

all condition distirbution are almost equal except for green an blue eyes which is higher for female for green eyes and higher for males for blue eyes.

A B C D blue Brown green Hazel Total Fc male 370 352 198 187 1107 F female 359 290 110 160 919 Total 729 642 308 347 2026

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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