NTD Consulting Partners conducted a survey of top executives that found that that 35% of them regularly read Time magazine, 20% read Newsweek, and 40% read U. S. News & World Report. A total of 10% read both Time and U. S. News & World Report. What is the probability that a particular top executive reads either Time or U. S. News & World Report regularly?

To solve this question you have to use the Addition rule which represents the probability that two events take place separately or at the same time. Here we have 3 events (Magazines) each one with a probability:

P (Time) = 35% = 0.35

P (Newsweek) = 20%=0.20

P (U. S. News & World Report) = 40% = 0.40

The problem also gives the probability of Times and U. S. News & World Report magazine together:

P (Times ∩ U. S. News & World Report) = 10% = 0.10

Then, to know the probability that a particular top executive reads either Time or U. S. News & World Report regularly we have to sum the probabilities of Time and U. S. News and subtract the probability of readers of both:

P (Times ∪ U. S. News & World Report) =

P (Times) + P (U. S. News & World Report) - P (Times ∩ U. S. News & World Report)

P (Times ∪ U. S. News & World Report) = 35% + 40% - 10%

P (Times ∪ U. S. News & World Report) = 65%