In the manufacturing process for a certain jack et 82 have n

In the manufacturing process for a certain jack

et, 82% have no defects, 14% have a minor defect an

d can be sold at an

outlet store and 4% have a major defect and are dis

carded or donated to charity. If 40 of these jacke

ts are selected at

random, what is the probability that at least 33 ha

ve no defects, at least 5 have a minor defect and a

t least 1 has a major

defect? (Again there are several cases to consider.)

Given p1=P(ND)=0.82; p2=P(Minor D)=0.14; p3=(M D)=0.04

n=40

we need Atleast 33 ND, 5 Minor D and 1 MD. This can be achieved from total 40 selected as follows

33 ND , 5Minor D, 2 MD or 33ND 6 Minor D, 1 MD or 34ND, 5 Minor D, 1 MD

Required probability is =P(33 ND , 5Minor D, 2 MD)+P( 33ND 6 Minor D, 1 MD ) +P( 34ND, 5 Minor D, 1 MD)

=0.04824+0.05627+0.05817=0.16268