please show steps and equations used Question 5.11 Marks The accompanying table

Question

please show steps and equations used

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 Male 373 357 211 78 1119 Female 314 295172 161 942 Total 687 652 383 339 2061 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(Me) b) 2 marks Calculate P(MCD c) 12 marks] Calculate P(MC) 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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