Event A occurs with probability 0.3. Event B occurs with probability 0.5. If A and B are independent, what is the probability that event A or event B occurs?
A. 0.15 B. 0.20 C. 0.65 D. 0.80 E. 0.92
The correct answer is (C).
In order to find the probability that A or B occurs, we use the formula P(A or B) = P(A) + P(B) – P(A and B). Remember that to find P(A and B) , we only have to multiply the two probabilities together, since A and B are independent events.
Substituting, we get P(A or B) = 0.3 + 0.5 – (0.3)(0.5) = 0.3 + 0.5 – 0.15. This becomes 0.8 – 0.15, which is 0.65, choice (C).
Note that if we were to simply add P(A) + P(B) to get an answer of 0.8, we would have doublecounted the event when A and B occur at the same time. That is why we had to subtract their overlap once, to get rid of the doublecounted overlap.  It states that the events are independent and nowhere does it state that they can occur together so why would you subtract the (.3)(.5) after you have .8 ?
