probability and applied statistics three companies are bidding on a contract . the relative qualities of the companies are such that company A is twice as good as company B and company B is three times as good as company . what is the probability of each company winning the contract ?

Hint: Assuming that a how good a company is, is precisely it's probability of winning the contract (as it is mentioned in the comments), then we have that $$P(A)=2P(B)$$ and $$P(B)=3P(C)$$ and $$P(A)+P(B)+P(C)=1$$ Thus $$P(A)=2(3P(C))=6P(C)$$ which gives $$6P(C)+3P(C)+P(C)=1$$