Question

A student wrote a (machine learning) algorithm for distinguishing between pictures of cats and pictures of dogs. The error rates of her algorithm are given as:

P(alg dog pic cat) = 0.1 P(alg cat pic dog) = 0.2.
[For example, P(alg cat pic dog) denotes the probability that the algorithm outputs "cat" when seeing a picture of a dog.]
Now we test the algorithm for several rounds, each round inputting to it a random picture of either a cat or a dog. For each picture, the probability of it being a cat's picture is 0.3 and the probability of it being a dog's picture is 0.7.
a) What is the probability that the algorithm correctly classifies 3 consecutive pictures? _____

Answer 1

The probability that the algorithm correctly classifies 3 consecutive pictures is 0.648.

Step-by-step explanation:

To find the probability that the algorithm correctly classifies 3 consecutive pictures, we can use the multiplication rule for independent events. Since the algorithm's errors are given in the form P(alg dog pic cat) and P(alg cat pic dog), we can calculate the probability of the algorithm classifying all 3 pictures correctly as:

P(correct classification) = P(alg dog pic dog) * P(alg dog pic dog) * P(alg cat pic cat) = 0.9 * 0.9 * 0.8 = 0.648