 # Probability

Which of the following statements about the defining properties of probability is TRUE? A) If the device that generates an event is not fair, the events can be mutually exclusive and exhaustive. B) The probability of any event is between 0 and 1, exclusive. C) The sum of the probabilities of events E1 though Ex equals one if the events are mutually exclusive or exhaustive. D) Mutually exclusive means that events share outcomes.

answer C b is wrong because it is 0 and 1 inclusive. d. mutually exclusive - have outcomes that are unique and distinct. a. if event is not fair, it is not probability!!

I have no idea what they mean by A (“device that generates an event”?) or C (“E1 through Ex”?). B and D are certainly not true. Edit: I don’t know about C. Whatever those events are, “mutually exclusive and exhaustive” is more likely to give you probability 1 than “mutually exclusive or exhaustive”

Definitely C…the rest don’t seem anywhere near the correct answer to me. =)

Joey, i think E1 through Ex means the number of outcomes? like outcome 1-5? means outcome 1,2,3,4,5…

This is just a screwed up question. An “event” in probability land is an outcome of some probabilistic experiment, say flipping a coin one hundred times or observing the price path a stock takes. I don’t know what it would mean to say that the device that generated the stock price path is not fair.

i guess when drawing up white/black balls from a bowl you would sneak a peak Your answer: C was incorrect. The correct answer was A) If the device that generates an event is not fair, the events can be mutually exclusive and exhaustive. Even if the device that generates an event is not fair, the events can be mutually exclusive and exhaustive. Consider a standard die with the possible outcomes of 1,2,3,4,5 and 6. The P(2 or 4 or 6) = 0.50 and P(1 or 3 or 5) = 0.50, and thus the probabilities sum to 1 and are mutually exclusive and exhaustive. An unfair die would not change this. The other statements are false. The probability of any event is between 0 and 1, inclusive. It is possible that the probability of an event could equal 0 or 1, or any point in between. The sum of the probabilities of events E1 though Ex equals 1 if the events are mutually exclusive and exhaustive. Mutually exclusive means that events do not share outcomes.

i guess we need to be more carefull