Question

A newly developed artificial intelligence has trouble distinguishing hand-written numbers from hand-written alphabets. There are pictures of 70 hand-written numbers and 30 hand-written alphabets mixed together for testing. Given that a hand-written number was shown, there is a 60% chance that artificial intelligence categorizes it as a number and a 40% chance that artificial intelligence categorizes it as an alphabet. Given that a hand-written alphabet was shown, there is an 80% chance that artificial intelligence categorizes it as an alphabet and a 20% chance that artificial intelligence categorizes it as a number. Assume that the pictures were randomly selected from the testing file. Given that the artificial intelligence categorizes a picture as a number, what is the probability that actually a hand-written number was shown.

Answer 1