Ch 2 - 102E

Chapter 3, Problem 102E

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QUESTION:

The accompanying table categorizing each student in a sample according to gender and eye color appeared in the article "Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask" (J. of Statistics Educ., 2013, Vol. 21, Num. 2).

Suppose that 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 represent the events that he or she has blue, brown, green, and hazel eyes, respectively.

a. Calculate both P(F) and P(C).

b. Calculate \(P(F\ \cap\ C)\). Are the events F and C independent? Why or why not?

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 female, what is the probability that she has green eyes?

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QUESTION:

The accompanying table categorizing each student in a sample according to gender and eye color appeared in the article "Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask" (J. of Statistics Educ., 2013, Vol. 21, Num. 2).

Suppose that 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 represent the events that he or she has blue, brown, green, and hazel eyes, respectively.

a. Calculate both P(F) and P(C).

b. Calculate \(P(F\ \cap\ C)\). Are the events F and C independent? Why or why not?

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 female, what is the probability that she has green eyes?

ANSWER:

Answer : Step 1 : The accompanying table categorizing each student in a sample according to gender and eye color appeared in the article. The table is given below. Eye Colour Gender Blue Brown Green Hazel Total Male 370 352 198 187 1107 Female 359 290 110 160 919 Total 729 642 308 347 2026 From the above table we consider A = blue B = Brown C=Green and D=Harzel. Let F denote the selected individual is a female. a). We have to calculate both P(F) and P(C). Here the total number of females is 919 and The total number of eye colour is 2026 Number of females So P(F) = Total number Number of females P(F) = Total number P(F) = 919 2026 P(F) = 0.4536 Here green = C So P(C) = Number of green Total number Number of green P(C) = Total number 308 P(C) = 2026 P(C) = 0.152 Hence P(F) = 0.4536 and P(C) = 0.152

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