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?

## Good businessman turns bad - a probability problem

### Good businessman turns bad - a probability problem

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

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

Maybe you mean three unsatisfactory product in the third line?