probability question

Question

1. A market-research firm monitored 1000 television viewers, consisting of 800 adults and 200 children, to evaluate a new comedy series that aired for the first time last week. Research indicated that 250 adults and 148 children viewed some or all of the program. If one of the 1000 viewers was selected, what is the probability that

c) the viewer was an adult or someone who watched the new program?

My answer was 398/1000 = 199/500 = 0.398 (the adults and children who actually watched the program out of the 1000) But the answer says is 0.948, why is that?

Answer 1

This question asks to calculate the OR probability of two non mutually exclusive events. If we call these events A and B, then the the probability for two non mutually exclusive events is:

P(A OR B) = P(A) + P(B) - P(A AND B)

In your example this works out to be:

P(Adult OR Watcher) = P(Adult) + P(Watcher) - P(Adult AND Watcher)

P(Adult OR Watcher) = 800/1000+ (250+148)/1000 - 250/1000 = 0.948