CareerCup

P(g) = probability of getting a good chip.

P(G) = probability of picking good company
P(B) = probability of picking bad company

Q: P(g) = P(G) * P(g|G) + P(B) * P(g|B) = 1/2 * 0.8 + 1/2 * 0.2 = 0.5

I was thinking along this lines: if you have 100 chips from both companies, 80 good and 20 bad chips will come from 1st (good ) company, and 80 bad and 20 good chips will come from 2nd (bad) company. So from 200 available chips there is 100 good and 100 bad chips. Then answer is 50 %, as probability to get good chip is (0.8 + 0.2)/2 = 0.5 or 50%

The probability tree is a binary tree with 2 levels (not considering 0 level) and 4 branches till leaf.
The below branches of the probability tree gives the answer
Probability = pGoodCompany * 80/100 + pBadCompany * 20/100
Now pGoodCompany = pBadCompany = 1/2.
So probability is 50%

P(Good) = P(Good|A)*P(A)+P(Good|B)*P(B)