Simple conditional probability problem

[theBEAST]

Homework Statement

There are two types of cooking oil, mono- and polyunsaturated. In a supermarket, 10.526% of the oil sold is mono-, of this 3.684% is canola oil and 6.842% is corn oil. The remaining 89.48% of the oil sold is poly-, of this 48.95% is canola oil and 40.53% is corn oil.

Given that the oil chosen is poly-, what is the probability that it is canola oil?

Homework Equations

P(A|B) = P(A∩B) / P(B)

The Attempt at a Solution

P(A∩B) means probability of A and B occurring at the same time but I don't think they can occur at the same time? Does this mean my relevant equation is false?

Intuitively I feel like the answer is just P(canola|poly) / [(P(canola|poly) + P(corn|poly)]. So (48.95)/(48.95+40.53).

 

[D H]

Your relevant equation and your answer are correct but your reasoning and your nomenclature are incorrect.

P(canola|poly) is not 48.95%. P(canola|poly) is what the problem is asking you to solve. That 48.95%? That's P(A∩B) where A=canola and B=poly. That brings up a problem with your reasoning. Oil can be both canola oil (event A) and polyunsaturated (event B).