Problem 3. Al is using his new machine learning algorithm to distinguish cat images from noncat images. 0 If the input image is a cat, there's a probability fneg that the algorithm will think it is not a cat. These are false negatives. o If the image is not a cat, there's a probability fpOS it thinks it is a cat. These are false positives. Al uses his algorithm on many input images, where a fraction c of them are cats (but he doesn't know which ones). (a) Suppose a random image is identied as a cat. What is the probability the image is actually a cat? Express answer in terms of fneg, fpos, c. (b) Suppose fneg = 0. In other words, any input image that is actually a cat will always identied as a cat. A random image is identied as a cat. If c = 0.1, what is the probability this image is actually a cat, in terms of fpos? How low would fpos have to be, to ensure this probability is 0.9 or higher