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 Post subject: GRE ProbabilityPosted: Sun Dec 23, 2012 4:22 am

Joined: Tue Jan 15, 2013 3:59 am
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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

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 double-counted 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 double-counted overlap.
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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 ?

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 Post subject: Re: GRE ProbabilityPosted: Sun Dec 23, 2012 4:54 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498

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