# Probability problem?

A store asks to it's providers for an article every thing they run out of those articles after selling the last unit. The sales are individual. There are 4 articles of the brand B, which's sale probability is 0.45 and 5 of the brand A, which's sale probability is 0.55. What are the chances they need to ask for new articles of the brand B after the 4th sale?

Relevance

The items could sell in various orders:

AABA ...

BAAB ...

BBAA ...

etc.

the one we are interested in is

BBBB

If the given probabilities hold even after some articles are sold,

then the probability of selling all the B's in a row is simply

(0.45)^4 = .041 or about 4.1%

Alternative way to look at it:

we might say: at any time, any of the remaining items is likely to be sold.

4 B's (4/9 probability = .444444)

5 A's (5/9 probability = .555555)

These numbers are close to what is given.

Then after the first sale, there are only 8 items left

and there are new probabilities, x/8 and y/8 where

x = number of B's left and y = number of A's, x+y = 8.

Then the probabilty of BBBB is

4/9 x 3/8 x 2/7 x 1/6 = 24 / 3024 = .0079 or 0.79 %