What is the Probability

Question

For a few weeks, a music producer kept track of newly released songs on a music streaming website. He recorded the music genre and number of times the song was played on its release date.

The probability that a song was rock is 0.42, the probability that it had 0-500 plays is 0.53, and the probability that it was rock or had 0-500 plays is 0.9.

What is the probability that a randomly chosen song was rock and had 0-500 plays?

Answer 1

Let's create notation:

P(A) - probability the song is rock

P(B) - probability the has 0-500 plays

P(A) = 0.42

P(B) = 0.53

P(A or B) = 0.9

Using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

0.9 = 0.42 + 0.53 - P(A and B)

P(A and B) = 0.05