Question

A shop sells one new designed jacket. Of the customers who buy this jacket, 50% choose the color black, 30% choose dark blue, and 20% choose green. Assume choice of color is made independently by different customers. 1. Calculate the probability that among the next 10 customers who buy the jacket, the first 6 will choose black jackets and the next 4 will not choose black jackets. 2. Calculate the probability that exactly one of the next 10 customers who buy a jacket will choose the green one.

Answer 1

P[ buy black jacket ] = 50% = 0.5

P[ buy dark blue jacket ] = 30% = 0.3

P[ buy green jacket ] = 20% = 0.2

Since, choices are made independently

1. Calculate the probability that among the next 10 customers who buy the jacket, the first 6 will choose black jackets and the next 4 will not choose black jackets.

P[ 6 will buy black jacket and next 4 will not buy black ] = P[ 6 will buy black jacket ]*P[ 4 will not buy black ]

P[ 6 will buy black jacket ] = 0.5^6 = 0.015625

P[ 4 will not buy black ] = Selecting 4 jackets and none is black = (1-0.5)^4 = 0.5^4 = 0.0625

P[ 6 will buy black jacket and next 4 will not buy black ] = 0.015625*0.0625

P[ 6 will buy black jacket and next 4 will not buy black ] = 0.0009765

2. Calculate the probability that exactly one of the next 10 customers who buy a jacket will choose the green one

P[ Exactly one will buy green jacket ] = P[ one will buy green jacket ]*P[ 9 will not buy green ]*10 ( as any of the 10 customer can buy green ]

P[ one will buy green jacket ] = 0.2

P[ 9 will not buy green ] = ( 1- 0.2 )^9

P[ 9 will not buy green ] = 0.1342

P[ Exactly one will buy green jacket ] = 10*0.2*0.1343

P[ Exactly one will buy green jacket ] = 0.2684