This is a problem from GRE quantitative section practice book.

The probability of rain in Greg's town on Tuesday is $0.3$. The probability that Greg's teacher will give him a pop quiz on Tuesday is $0.2$. The events occur independently of each other.

Quantity A The probability that either or both events occur

Quantity B The probability that neither event occurs

First, let the probability of rain $P(R)$ and the probability of pop quiz $P(Q)$.

Then A is asking for $P(R \cup Q)$ so it would be 0.3+0.2-0.3*0.2=0.44

and since B is asking for the complement of A, it would be 0.56.

This is my reasoning, however the solution I'm looking at says both are 0.56. It says that A should be 0.3+0.2+0.06 since the probability of either events occuring is 0.2+0.3 and the probability of both events is 0.06. But I think the interpretation of either or both events is the union of two events. Which interpretation is correct?

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    $\begingroup$ Given the wording, I'll side with you, except that I'll calculate $P(B)$ first as $(1-0.2)(1-0.3)$ then $P(A)=1-P(B)$. Are the question and solution both directly from ETS or one of those test prep companies? $\endgroup$ – Kim Jong Un Sep 10 '14 at 15:52

The interpretation given by the practice exam is incorrect as adding the probability of both events happening overall double counts that event as you've probably already knew.

This interpretation is clearly bogus if you increase both event's probability to 50%: Going by the practice book's explanation, then the probability of both events happening should be 125% which is obviously not true.

Which practice book is this coming off from btw?


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