# Probability of “either/or” and “neither” for two independent events

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?

• 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? – Kim Jong Un Sep 10 '14 at 15:52