Question

Henry is a quality control inspector. He is watching the production line for Barb's Raisin Cookie. Henry will reject a cookie with less than 8 raisins. In the past, one out of every 100 cookies had less than 8 raisins. Find the probability that the first cookie Henry rejects is the 5th cookie on the line.

Answer 1

Let X be random varaible of no of cookies passed before rejecting 1st coockie with less than 8 rains ,on the production line by Henry

X~Geometric (P)

As in past henry rejected one out of every 100 cookies which had  less than 8 rains

p=0.01

X~ Geo (P=0.01)

pmf of X is

As first cookie Henry rejects is 5th coockies on line.It means 4 cokies passed before rejecting 1st coockies with less than 8 rains

hence probability that 1st coockies Henry rejects is 5th coockies on line is

P(X=4) =0.0096------------------------------ans