1. Find the probability of obtaining exactly one head when flipping four coins. 2. Calculate the number of ways to arrange the letters in your: a. First name. b. Last name. c. The letters in both your first name and last name. 3. In a company, there are 28 total employees. All employees who have worked there for more than five years receive a gift. a. If eleven employees have received the gift, what is the probability that a randomly selected employee has received the 5-year gift? b. Describe (in words) the complement of the group of employees who have received the 5-year gift? c. Determine the probability that a randomly selected employee has not received the 5- year gift? 4. Out of a class of 30 students, there are 16 students who study Latin, 21 who study German, and 7 who student both. What is the probability that a randomly selected student from the class will study only Latin? 5. During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to always foul their opponent's tall forward. Because he is so tall, he makes 57% of shots he takes close to the basket. However, when he is fouled, his free-throw shooting percentage is only 51.5%. The shots he makes close to the basket are worth two points and each of the two free throw shots after being fouled are worth one point. a. Calculate the expected value of the number of points the forward makes when he takes a shot close to the basket. b. Calculate the expected value of the number of points the forward makes when he hoots two foul shots. c. Based on these expected values, is fouling the tall forward a good strategy? Explain your answer. 6. The test scores for MAT143 students are given below 75, 77, 79, 72, 69, 71, 73, 77, 78, 81, 43 a. Find the mean test scores. b. Find the median test score. c. Which measure of center tendency better describes the data? 7. Ava scored a 92 on a test with a mean of 71 and a standard deviation of 15. Charlotte had a score of 688 on a test with a mean of 493 and a standard deviation of 150. Which score was better with respect to their test