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?

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 ‹‚ 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?
e. What is the "conditional distribution" of eye color for females (i.e., P(A|F), P(B|F), P(C|F), and P(D|F)), and what is it for males? Compare the two distributions.

Eye Color Gender Blue Brown Gree Haz Total Male 370352 Female 359 290 Total729642308347 2026 198 187 1107 110 160 919

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