probabilities finite

Question

 involving a movie critic reviewing films. Assume that the critic finds that 40 percent of the movies have positive comments about the plot, 50 percent have positive comments about the acting, and 25 percent were not given positive comments about either plot or acting.

What is the probability that a randomly selected movie was given positive comments about both plot and acting? 

Answer 1

Let A, P denote the events of receiving positive reviews in acting and plot, respectively. We have probabilities given as: P(A) = 0.5, P(P) = 0.4, and P(A U P) = 1 - 0.25 = 0.75. We need to find P(A intersection P). By the principle of inclusion-exclusion:

P(A U P) = P(A) + P(P) - P(A intersection P)

Substituting the given values in this equation,

0.75 = 0.5 + 0.4 - P(A intersection P)

Solving for the unknown, we finally get P(A intersection P) = 0.15.