A group of students are shown a picture. They can either say that the picture is an oil painting or water color painting. If they are not sure, they can say undecided.

Now, it is a well-known fact that this museum holds 70% oil paintings, 17% water color paintings, and the rest is some other type of painting.

Students can correctly classify oil and water color paintings 80% of the time, and all other types of paintings are always classified as undecided.

Oil and Water color paintings are classified as undecided 10% of the time.

Calculate the probability that a randomly chosen painting is an oil painting?

Suppose that the selected painting is an oil painting, what is the probability that it is actually a water color painting?