Mathematical Explorations- complete module 5 and module 6 separate critical thinking assignments

Module 5 Critical Thinking- Counting Principles

Question #1
How many ways can two slices of pizza be chosen from a plate containing one slice each of pepperoni, sausage, mushroom, and cheese pizza.

Question #2
A bowl of candy contains many pieces of candy, but only six different types of candy. How many ways can three pieces of candy be removed from the bowl? (Assume you can remove one or more pieces of the same type of candy.)

Question #3
Each conference of the National Football League consists of sixteen teams. If we assume there were no ties, the top three teams in a conference could be determined from their win-loss records. How many different outcomes are possible for this top-three team list?

Requirements:

• Show all your work so that the instructor clearly sees how you solved the problem.
• Make sure your final answer is clear and visible.
• provide as much detail possible in your explanations and show all work. If you use sources make sure to include a reference page and cite the sources within text.

Module 6 Critical thinking assignment 2- Probability

Question #1
Three fair coins are flipped. Outcomes in the sample space are represented by strings such as HHT, HTH, and TTT.

• List all of the elements in the sample space.
• Express the event “two of the three coins are heads” as a set. Show each of the possible combinations.
• What is the probability that two of the three coins are heads?

Question #2
Three cards are selected from a 52-card deck of cards. What is the probability of choosing three jacks?

Question #3
The odds of losing money on a particular stock is 8 to 2. What is the probability that money will be lost on the stock?

Requirements:

• Show all your work so that the instructor clearly sees how you solved the problem.
• Make sure your final answer is clear and visible.
• provide as much detail possible in your explanations and show all work. If you use sources make sure to include a reference page and cite the sources within text.