Question 5. 11 Marks] The accompanying table categorizes each student in a sampl

Question

Question 5. 11 Marks] The accompanying table categorizes each student in a sample according to gender and eye colour. Eye Colour Gender Blue Brown Green Hazel Total 211 178 1119 295172161 942 383 339 2061 Male 373 357 Female 314 Tota 687 652 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) [2 marks Calculate P(Mc). b) 2 marks Calculate P(M D) c) [2 marks Calculate P(MICC) d) [2 marks] If the selected individual is female, what is the probability that she has brown eyes? e) 3 marks] Are the events M and A independent? Why or why not?

Explanation / Answer

aP(Mc) =1-P(M) =1-1119/2061 =0.4571

b) P(Mc|D ) =161/339 =0.4749

c)

P(M|Cc) =(373+357+178)/(687+652+339)= 0.5411

d)

P(B|Mc) =295/942=0.3132

e) here P(M)*P(A) =(1119/2061)*(687/2061)=0.18098

and P(M & A) =373/2061 =0.18098

as they both are equal ; therefore M and A are independent.

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