Games have been an enjoyable pastime for many years.  Families and friends have gathered to play board games, card games and dice games like Yahtzee, Poker, and Monopoly.

The goal of this project is to analyze different classic games for the probability that occurs in them.  You may work alone or with a partner.

Your job:

  1. Pick a classic game à Blackjack
  2. Analyze the probability of different events that can occur in the game.  You need to find 5 different probabilities giving a specific example from different aspects of the game.  Then calculate the probability that this event occurs.  You need to have one of each: basic probability, addition, multiplication, permutation and combination. 

For example: The game of LIFE. 

  • Basic: We could evaluate probability with the spinner (Probability you spin a 5).
  • Addition: salary cards (Probability your salary is $125,000 or $250,000).                    
  • Multiplication: LIFE tiles (Probability you draw a $100,000 and a $50,000 tile).                            
  • Permutations: the number of ways to order 5 people in the car.
  • Combination: When we played LIFE and had to draw a card for a life event (payday, job, house) we had a house rule of drawing 3 cards and selecting the one we wanted. How many combinations of 3 cards can you get from the house cards?
  • Type a report with all of your findings and probability questions and answers that you have decided to investigate. 
  • Be sure to be careful with card games that have draw and discard piles.  This impacts your probabilities as cards are discarded between turns, which then limits the number of possibilities.  Also be sure you are accounting for other players in those situations. 

Your project must include:

  1. An introduction paragraph explaining the game/rules/cards/dice or whatever is used in the game
  • A paragraph for each probability problem.  Be specific with what it is you are finding, how it is found as well as the final answer.  Please remember that a paragraph is roughly 5 sentences. You need to explain all the numbers and work that lead to get to the answer to the question you posed in the first sentence.
  1. An example Paragraph For the game of Monopoly: What is the probability that I roll doubles or a sum of 5 on my turn in the game of monopoly? This would be an example of addition probability with disjoint events as neither of these outcomes can happen at the same time. That means to find the P(doubles or sum of 5) = P(doubles)+P(sum of 5). First to find the P(doubles) we know we can roll 1,1; 2,2; 3,3; 4,4; 5,5; or 6,6. This is 6 possibilities out of the total outcomes 36 for rolling two dice. Second to finding P(sum of 5). This can be done by rolling 1,4; 2,3; 3,2; or 4,1 which is 4 possibilities out of 36. This means that  ( doubles or sum of 5) = P(doubles)+P(sum of 5) = 6/36+4/36 = 10/36 = 5/18. This means there is a 5/18 or about a 28% chance that I will roll doubles or a sum of 5 on my next turn. 
  • Times New Roman Font, 1 inch margins and be double spaced.

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