Math solve

1. Determine the number of elements in the Sample Space for each of the following: a. Tossing a coin three times b. The order that the top 5 students will receive their diplomas. c. Tossing a pair of dice. 2. Determine the theoretical probability of a. Tossing two heads with two coins b. Rolling a 2 or 5 with one die 3. Design a probability experiment to determine the empirical probability of each of the events in question 2. Explain why your results may be different from the theoretical results you determined. How would you alter your experiment so that theoretical and empirical results become equal? 4. When a die is rolled 20 times, 4 came up 5 times. a. Determine the empirical probability of rolling a 4 with a die based on 20 trials. b. Determine the theoretical probability of rolling a 4 with a die. 5. What is the probability of not rolling an 11 with a standard pair of dice? What is the complement of this event? 6. A couple plans to have three children. a. Construct a tree diagram to illustrate the possible gender outcomes of the three children. b. Find the probability that the couple has i. 2 girls? ii. at least 2 girls? ili. a girl, then a boy, then a girl