Question

The following contingency table shows the number of customers who bought various brands of shoes at Amazon, Outlets and Macys (No Excel)

Brand	Amazon	Outlets	Macys
Nike	48	35	37
Adidas	36	24	30
UGG	25	12	44

Given that the shoes was purchased at Macys, the probability that it is Nike is______

(No Excel)

Answer 1

Consider the below table.

Brand	Amazon	Outlets	Macys	Total
Nike	48	35	37	120
Adidas	36	24	30	90
UGG	25	12	44	81
Total	109	71	111	291

P(Nike | Macys) = P(Nike Macys) / P(Macys)

                          =(37/291) / (111/291) .......(from table and P(A) = number of occurance of event A divided by the number of occurance of all events)

                          = 37 / 111

                          = 1 / 3 = 0.3333

The probability that it is Nike given that the shoes was purchased at Macys is 0.3333.