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Define the following terms: experiment, outcome, sample space, simple event, and compound event.

A test contains two multiple-choice questions. If a student makes a random guess to answer each question, how many outcomes are possible? Depict all these outcomes in a Venn diagram. Also draw a tree diagram for this experiment. (Hint: Consider two outcomes for each question- either the answer is correct or it is wrong.)

Draw a tree diagram for three tosses of a coin. List all outcomes for this experiment in a sample space \(S\).

Briefly explain the three approaches to probability. Give one example of each approach.

Which of the following values cannot be probabilities of events and why? \(\begin{array}{llllllll}1 / 5 & .97 & -.55 & 1.56 & 5 / 3 & 0.0 & -2 / 7 & 1.0\end{array}\)

Which of the following values cannot be probabilities of events and why? \(\begin{array}{llllllll}.46 & 2 / 3 & -.09 & 1.42 & .96 & 9 / 4 & -1 / 4 & .02\end{array}\)

Suppose a randomly selected passenger is about to go through the metal detector at JFK Airport in New York City. Consider the following two outcomes: The passenger sets off the metal detector, and the passenger does not set off the metal detector. Are these two outcomes equally likely? Explain why or why not. If you are to find the probability of these two outcomes, would you use the classical approach or the relative frequency approach? Explain why

Thirty-two persons have applied for a security guard position with a company. Of them, 7 have previous experience in this area and 25 do not. Suppose one applicant is selected at random. Consider the following two events: This applicant has previous experience, and this applicant does not have previous experience. If you are to find the probabilities of these two events, would you use the classical approach or the relative frequency approach? Explain why.

A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is \(\begin{array}{ll}\text { a. red? } & \text { b. green? }\end{array}\)

A random sample of 2000 adults showed that 1320 of them have shopped at least once on the Internet. What is the (approximate) probability that a randomly selected adult has shopped on the Internet?