Probability when I have one or 3 choices I'm wondering what is "better" to have in terms of profit:
Lets say we have 300 people come to your store and you have 3 products. Each individual is given (randomly) one product. If the individual likes the product he will buy it, but if he doesn't like the product, he will turn around and walk out of the store forever. 
Now, I'm wondering is it better (more probable) to have 3 products or just one, in order to maximize the total number of sold products.
Important to note is that customer doesn't decide which product he gets (he gets it randomly), he only decides if he likes it or not (50-50 chance he likes it).
Any help is welcome, or maybe link to some theory I should read in order to come p with a solution. 
edit:
Ok, so, a little detailed explanation: let say that I have unlimited number of each of the items in the store(currently 3 different items - but unlimited number of them in the stock), and lets say that each customer that comes in to my store (aproximatelly 1000 a day) either likes or doesn't like the randomly offered product to him. Each of the products offered is of the same popularity - we sold almost the same amount of product1, product2 and product3. Product1 sold for example just 100 more units than Product2 and Product 2 sold like 100 more units than Product3, but the sold numbers are as high as 1000000 so this difference is really very low. Does this now help in determining if we should chose only Product1 and keep forcing it, or should ve leave the three products as is?


is it better (more probable) to have 3 products or just one, in order to maximize the total number of sold products. Important to note is that customer doesn't decide which product he gets (he gets it randomly), he only decides if he likes it or not (50-50 chance he likes it).

Under the conditions you have described, the main objective is to maximize the total number of sold products. This number will be <= population number of 800.
The only factors here are:
1 - The number of people showing in the store
2 - The number of items you have in stock
factor 1 above is not described in your statement of the problem, but if you think that having more than 1 product will affect it then having 3 products is better than 1. Otherwise, the only factor would be factor (2) and adding new products will not add value.
I hope this helps.
