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In a statistics class of 42 students, 28 have volunteered for community service in the past. Find the probability that a randomly selected student from this class has volunteered for community service in the past.

The television game show The Price Is Right has a game called the Shell Game. The game has four shells, and one of these four shells has a ball under it. The contestant chooses one shell. If this shell contains the ball, the contestant wins. If a contestant chooses one shell randomly, what is the probability of each of the following outcomes? a. contestant wins b. contestant loses Do these probabilities add up to \(1.0 ?\) If yes, why?

Briefly explain the difference between the marginal and conditional probabilities of events. Give one example of each.

What is meant by two mutually exclusive events? Give one example of two mutually exclusive events and another example of two mutually nonexclusive events.

Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses. $$ \begin{array}{lcc} \hline & \text { Have Shopped } & \text { Have Never Shopped } \\ \hline \text { Male } & 500 & 700 \\ \text { Female } & 300 & 500 \\ \hline \end{array} $$ a. If one adult is selected at random from these 2000 adults, find the probability that this adult i. has never shopped on the Internet ii. is a male iii. has shopped on the Internet given that this adult is a female iv. is a male given that this adult has never shopped on the Internet b. Are the events "male" and "female" mutually exclusive? What about the events "have shopped" and "male?" Why or why not? c. Are the events "female" and "have shopped" independent? Why or why not?

There are 142 people participating in a local \(5 \mathrm{~K}\) road race. Sixty-five of these runners are female. Of the female runners, 19 are participating in their first \(5 \mathrm{~K}\) road race. Of the male runners, 28 are participating in their first \(5 \mathrm{~K}\) road race. Are the events female and participating in their first \(5 \mathrm{~K}\) road race independent? Are they mutually exclusive? Explain why or why not.

Define the following two events for two tosses of a coin: \(A=\) at least one head is obtained \(B=\) both tails are obtained a. Are \(A\) and \(B\) mutually exclusive events? Are they independent? Explain why or why not. b. Are \(A\) and \(B\) complementary events? If yes, first calculate the probability of \(B\) and then calculate the probability of \(A\) using the complementary event rule.

The probability that a randomly selected college student attended at least one major league baseball game last year is .12. What is the complementary event? What is the probability of this complementary event?

Explain the meaning of the intersection of two events. Give one example.

What is meant by the joint probability of two or more events? Give one example.