A distribution center receives shipments of a product from three different factories in the following quantities: 50,35, and 25. Three times a product is selected at random, each time without replacement. Find the probability that none of the three products came from the third factory.

Question

perl · Answer

Welcome to open study  :)
the total products are 50 + 35 + 25 = 110

anonymous · Answer

yes. Factory 1=50, Factory 2=35, Factory 3=25, how do I figure out the probability that none of the three products come from factory 3

perl · Answer

P(none of the three products came from the third factory)=1-P(all three products came from the third factory)

perl · Answer

$$ \large P(A) = 1 - P(A' )  \
=1 - \frac{25}{110}\frac{24}{109}\frac{23}{108}

$$

anonymous · Answer

i think i figured it out. is it (85/110)X(84/109)X(83/108) 
therefore taking away the 25 products from factory 3 and finding the total: 85, then finding probability as you take one product without replacing it until you get the three products. equaling 0.458

anonymous · Answer

yeah for some reason those equations freak me out. i'm better at putting it in words. is that right?

perl · Answer

thats incorrect

anonymous · Answer

that is the answer it gives in my textbook.

perl · Answer

$$

\Large =1 - \frac{25}{110}\frac{24}{109}\frac{23}{108} = 0.98934


$$

perl · Answer

this is the probability that none of the three products came from the third factory

perl · Answer

(85/110)X(84/109)X(83/108)  is the probability that all three products came from factory 1  or factory 2

anonymous · Answer

but combined. maybe i worded the question wrong when i asked you but the answer they are looking for is .458 thanks for your help! it did help to talk it out with someone

perl · Answer

its wrong , here you can check this https://answers.yahoo.com/question/index?qid=20110929100443AATx6QY

anonymous · Answer

no, sorry i'm going by the answer in my textbook. thank you though