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What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean the event is impossible?

What method of assigning probabilities to a simple event uses relative frequencies?

True or False: In a combination problem, order is not important.

True or False: In a probability model, the sum of the probabilities of all outcomes must equal 1 .

Suppose that you roll a pair of dice 1000 times and get seven 350 times. Based on these results, what is the probability that the next roll results in seven?

What does it mean when two events are complements? In Problems \(5-12,\) a probability experiment is conducted in which the sample space of the experiment is \(S=\\{1,2,3,4,5,6,7,8,9,\) 10,11,12\\}\(.\) Let event \(E=\\{2,3,4,5,6,7\\},\) event \(F=\\{5,6,7,8,9\\},\) event \(G=\\{9,10,11,12\\},\) and event \(H=\\{2,3,4\\} .\) Assume that each outcome is equally likely.

True or False: Probability is a measure of the likelihood of a random phenomenon or chance behavior.

Let the sample space be \(S=\\{1,2,3,4,5,6,7,8,9,10\\} .\) Suppose that the outcomes are equally likely. Compute the probability of the event: \(E=\\{1,3,5,10\\}\)

Determine whether the events \(E\) and \(F\) are independent or dependent. Justify your answer. (a) \(E:\) Speeding on the interstate. \(F:\) Being pulled over by a police officer. (b) \(E:\) You gain weight. \(F:\) You eat fast food for dinner every night. (c) \(E\) : You get a high score on a statistics exam. \(F:\) The Boston Red Sox win a baseball game.

Find the value of each factorial. \(10 !\)