Question

A machine learning model is designed to predict whether a given email is spam or not. The model has an accuracy of 95%, a false positive rate of 2%, and a false negative rate of 5%. If 10% of all emails received are spam, what is the probability that an email identified as spam by the model is actually spam?

Answer 1

To find the probability that an email identified as spam by the model is actually spam, we can use Bayes' Theorem. The probability is 0.15.

Step-by-step explanation:

To find the probability that an email identified as spam by the model is actually spam, we can use Bayes' Theorem. Let's define the events:

Bayes' Theorem can be written as:

P(B|A) = (P(A|B) * P(B)) / P(A)

In this case, P(A) is the probability that an email is identified as spam, which is equal to the sum of the probability of true positives (1 - false negative rate) and the probability of false positives (false positive rate * probability of non-spam emails). P(A) = (1 - 0.05) * 0.1 + 0.02 * 0.9 = 0.065.

P(B) is the probability that an email is actually spam, which is 0.1.

P(A|B) is the probability of true positives, which is 1 - false negative rate = 1 - 0.05 = 0.95. Plugging in these values, we have:

P(B|A) = (0.95 * 0.1) / 0.065 = 0.15

Therefore, the probability that an email identified as spam by the model is actually spam is 0.15.