The accompanying table categorizes each student in a sample according to gender

Question

The accompanying table categorizes each student in a sample according
to gender and eye colour.
Suppose that one of these 2061 students is randomly selected, let M denote the event that the
selected individual is male, and A, B, C and D represent the events that the selected student has
blue, brown, green and hazel eyes, respectively.
a- Calculate P(Mc). b-Calculate P(Mc|D).   c-Calculate P(M|Cc). d-If the selected individual is female, what is the probability that she has brown eyes?
e-Are the events M and A independent? Why or why not?

gender blue brown green hazel Total male 373 357 211 178 1119 female 314 295 172 161 942 Total 687 652 383 339 2061

Explanation / Answer

a) P(Mc) =1-P(of male) =1-1119/2061=0.45706

b)  P(Mc|D). =1-P(M|D) =1-178/339=0.474926

c) P(M|Cc) =P(M and Cc)/P(Cc) =(373+357+178)/(2061-383)=0.54112

d)probability that she has brown eye given female =295/942=0.313163

e) here P(M) =1119/2061 and P(A) =687/2061

also P(M and A) =373/2061

as P(M and A) is not equal to P(M)*P(A) ' therefore M and A are not independent,

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