Now that we know the basic probabilities of individual tags, we can also find the joint probabilities of some of these events. For instance, how often do a deciduous tree and a coniferous tree appear in the same painting? We know that 57 percent of paintings contain a deciduous tree and 53 percent of paintings contain a coniferous tree. According to our data set, 20 percent of paintings contain at least one of each.
What’s more, we can also find the probability that Ross painted something given that he painted something else, a statistic that’s called Conditional probability can be a bit tricky. We know that 44 percent of Ross’s paintings contain clouds, 9 percent contain the beach and 7 percent contain both the clouds and the beach. We can use this information to figure out two things: the probability that Ross painted a cloud The biggest pitfall people often face is assuming the two probabilities are the same. The probability that Ross painted a cloud given that he painted the beach — essentially, how many beach paintings have clouds — is (0.07)/(0.09), which is 78 percent. The vast majority of beach scenes contain clouds. However, the probability that Ross painted a beach given that he painted a cloud — or, how many cloud paintings contain a beach — is (0.07)/(0.44), or 16 percent. So the vast majority of cloud paintings don’t have beaches.
I figured out the conditional probability of every Bob Ross tag against every other tag to answer the following pressing questions.
There’s a 93 percent chance that Ross paints a second tree given that he has painted a first.
About 39 percent prominently feature a mountain.
Ross was also amenable to painting friends for mountains. Sixty percent of paintings with one mountain in them have at least two mountains. |