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?
- MathMan TGLv 71 decade agoFavorite Answer
The items could sell in various orders:
the one we are interested in is
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 %