Let's look at the possibilities: has oil and oil found, has oil but not found, no oil and not found, no oil and false positive.
There is a 45% chance of the land having oil. There is also an 80% chance that the kit will give an accurate reading. If the test says that there is no oil, then for the land to have oil, the 45% chance would have to be true (since the land has oil), and the test would have to failed (20%) chance. We can multiply these two chances together like with any other combination of chances to find our solution:
45% x 20% = 0.45 x 0.2 = 0.09
Therefore, there is only a 9% chance that the land will have oil if the kit claims it doesn't.
