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 Post subject: GRE Probability
PostPosted: Sun Dec 23, 2012 4:22 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

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 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 Probability
PostPosted: Sun Dec 23, 2012 4:54 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
The probability of occurrence of an event implies that we consider limited time interval. By the end of that time we are able to say if the event has occurred or not.

For example, when we consider a flip of a coin we know if the event occurred or not as soon as we see the result of the flip; considering the probability that it will rain tomorrow we will know if the event occurred or not by the end of the next day.

Quote:
It states that the events are independent and nowhere does it state that they can occur together
Thus when we speak of "the probability that event A or event B occurs", we consider time interval, which ends with the moment when we know that each event either has occurred or not.

For example,
Event A: It will rain in Botswana today.
Event B: It will snow in London the day after tomorrow.

As you see these events cannot happen at the same time. But since we are considering the probability that event A or event B occurs, we are considering the outcome by the end of the day after tomorrow. Then we will definitely know if each of the events has occurred or not.

Another example:
Event A: We get heads, when we flip the red coin.
Event B: We get tails, when we flip the red coin.

We do not have to flip coins at the same time. But we calculate the probability before the flips take place and consider the outcome at the end of the second flip.


Independent events are events that do not affect each other's occurrence. So they can happen both, or none, or just one of them.


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