Question 1
Indicate true or false, and explain your reasoning (be sure to show all calculations):
a. If a die is rolled three times, the chance of getting at least one ‘6' is 1/6 + 1/6 + 1/6 =1/2.
b. If a coin is tossed twice, the chance of getting at least one tail is 25%.

Question 2
A person is chosen from the population of New York City residents. Let A be the event that the person chosen works full-time, and B be the event that the person chosen gets 10 hours of sleep per night. If the probability that a person works full-time is 0.23, the probability that a person gets 10 hours of sleep per night is 0.15, and the probability that a person works full-time or gets 10 hours of sleep per night is 0.38, which of the following is true? Show all calculations and explain your reasoning.
a) The events A and B are independent.
b) The events A and B are mutually exclusive.
c) The events A and B are both mutually exclusive and independent.
d) The events A and B are neither mutually exclusive nor independent.

Question 3
An article published in Science News reported on research concerning the effects of regular Internet usage. According to the article, 36% of Americans with Internet access are regular Internet users, meaning that they log on for at least 5 hours per week. Among regular Internet users, 25% say that the web had reduced their social contact (e.g. talking with their family and friends or going out of town). What is the probability that a randomly selected American with Internet access is a regular Internet user who feels that the Web has reduced his or her social contact?

Question 4
According to a recent poll published in USA TODAY, roughly 54% of U.S. men and 33% of U.S. women believe in extraterrestial aliens. Of U.S. adults, roughly 48% are men and 52% are women.
a) What percentage of U.S. adults believe in such aliens?
b) What percentage of U.S. women believe in such aliens?
c) What percentage of U.S. adults that believe in such aliens are women?