# ECON 221 Business Statistics Vinison Midterm Review

What does it mean if I say that there is a 25% chance there will rain tomorrow?
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When using the addition rule to find the union between A and B, why do we subtract the intersection of A and B? Shouldn't we be able to just add P(A) and P(B)? Suppose that the probability of rain is 25%, the probability of wind is 10% and P(Rain ∩ Wind) = 5%. What is the probability that rain or wind occur? What is the probability that neither occur?
Suppose that the probability that the pool will be closed is 55%. If the probability that the pool will close conditional on rain is 85%, what does that mean about the relationship between rain and pool closings? If the probability of rain is 50%, What is the probability that the pool closes and it is raining?
How is the Bayes' Theorem derived? Suppose a patient is being tested for a disease. The probability of having the disease when you are tested is 50%. Suppose that the test is 99% accurate (if the patient has the disease the test will be positive 99% of the time). There is a 2% chance of a false positive. Given that the test is positive, what is the probability that the patient has the disease?