## Good businessman turns bad - a probability problem

For students of class 11-12 (age 16+)
Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

### Good businessman turns bad - a probability problem

Consider that a businessman has gained quite a good will and managed $X$ regular customers who will buy precisely one of his product each month. Now the businessman turns greedy and decides to make some quick profit. He brings $50\%$ bad products and mixes it randomly with the good products so that the product sold to any customer may be equally good or bad. A bad product might prove satisfactory with a probability of $p_1$. It is known that a client will stop buying products from that businessman if
-he finds one product unsatisfactory with probability $p_2$,
-he finds two products unsatisfactory with probability $p_3$ and
-he receives three products with a probability $1$
What is the expected number of customers left after three months?
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

abir91
Posts: 52
Joined: Sun Dec 19, 2010 11:48 am

### Re: Good businessman turns bad - a probability problem

Maybe you mean three unsatisfactory product in the third line?
Abir

Have you read the Forum Rules and Guidelines?