aleksandra
BAN USERI post my solution made with tree diagrams
--->(branch 1) Good Company, 0.5 ---> (subbranch 1) Good Chips, 0.8
---> (subbranch 2) Bad Chips, 0.2
----> (branch 2) Bad Company, 0.5 ---> (subbranch 1) Good Chips, 0.2
---> (subbranch 2) Bad Chips, 0.8
After we discovered that we got chips that is good, we can make another probability tree for the aposterior event. However, for the new tree, probability that we choose a Good company is higher, given the fact that the first chips is good. What is the P(Good Company|Good Chips)?
P(Good Company|Good Chips) = P(Good Company and Good Chips)/P(Good Chips) = (we read values from the upper tree) = 0.8*0.5/(0.8*0.5+0.5*0.2) = 0.8
Given the fact that the first chips is good, now we have 0.8 chance that we chose a good company. So we have another aposterior tree:
--->(branch 1) Good Company, 0.8---> (subbranch 1) Good Chips, 0.8
---> (subbranch 2) Bad Chips, 0.2
----> (branch 2) Bad Company, 0.2 ---> (subbranch 1) Good Chips, 0.2
---> (subbranch 2) Bad Chips, 0.8
We finally compute from the tree P(Good Chips) = P(Good Chips and Good Company) + P(Good Chips and Bad Company) = 0.8*0.8 + 0.2*0.2 = 0.68
I am sorry for posting my solution tree times, the system seemed to be blocked ://. Now it's impossible to erase it as I posted it as a guest firstly. BTW, instead of 0.64 it should be 0.68, miscalculation.
- aleksandra December 11, 2015