Answer each of the following problems. Make sure to show your work.


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1 Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her probability of winning the game, what is the sample space they must use? 2. A board game requires each player to draw a card. Each card has a different number on it. The player with the highest number wins. Is the probability of a player winning an independent or dependent event? Why? 3. A box contains 12 red pens, 14 blue pens, and 6 black pens. If a red pen is drawn first and kept out of the bag, what fraction represents the probability that a black pen will be drawn second? 4. A die has been rolled seven times in a row. Each time, the die landed on six. What is the probability that the die will land on six on the eighth roll? Why? 5. The probability that it will rain today is 70%. The probability that it will just be cloudy is 20%, and the probability that it will be sunny and clear is 10%. Is today s weather a biased event? 6. What is the probability that it will rain or that it will be sunny and clear?
2 7. If it rains, a gardener has a 40% chance of having a day off on the following day. If it doesn t rain, he has to work the next day. What is the probability that the gardener will have to work tomorrow? 8. What is the probability that each spinner will land on purple?
3 Use the following tree to answer questions What is the value of X? 10. What is the probability that Event D will be the outcome? 11. If A represents that it will snow and there will be a snow day, B represents that it it will snow and there won t be a snow day, C represents that it won t snow and there won t be a snow day, and D represents that it won t snow and there will be a snow day, what is the probability that there won t be a snow day? 12. What is the probability that there will be a snow day?
4 13. What probability model should be used when examining simple events? 14. A game involves drawing 16 red coins, 12 blue coins and 3 green coins from a bag. A player wins if they draw a blue or green coin and loses if they draw a red coin. Is this game fair? Explain your answer. 15. A game involves drawing 16 red coins, 13 blue coins and 3 green coins from a bag. A player wins if they draw a blue or green coin and loses if they draw a red coin. Is this game fair? Explain your answer. 16. What model should be used when performing complex probability calculations with multiple AND functions? Explain your answer. 17. At a given company, an employee is 42% likely to be male and 58% likely to be a female. An employee is also 30% likely to be an engineer, 50% likely to be a manager, 25% likely to be a researcher and 10% likely to be a technical writer. If Event A = male manager or male engineer, what is event A? 18. At a given company, an employee is 42% likely to be male and 58% likely to be a female. An employee is also 30% likely to be an engineer, 50% likely to be a manager, 25% likely to be a researcher and 10% likely to be a technical writer. What is the probability of the union of being an engineer or a technical writer?
5 19. Given Event A, Event B, and Event C. Event A and Event B are mutually exclusive. Event A and Event C are not mutually exclusive. P(A) = 0.45 P(B) = 0.35 P(C) = 0.25 What is the probability of the complement of Event B? 20. Given Event A, Event B, and Event C. Event A and Event B are mutually exclusive. Event A and Event C are not mutually exclusive. P(A) = 0.55 P(B) = 0.35 P(C) = 0.66 What is the probability of the complement of Event A C? 21. What is the probability that a person will flip a coin three times and that it will land heads up three times in a row? 22. A friend offers to play a game where you pay him $2 if the roll of a 6sided die comes up at 1, 2, 3, or 4, and he pays you $3 if the die comes up a 5 or 6. What is the expected value of a round for you if you play the game?
6 23. Below is a spinner. What is the probability of landing on a number divisible by 2? 24. Using the spinner below, what is the probability of landing on a number divisible by 2 twice in a row? 25. If there is an event in which three decisions must be made and there are four choices available for each decision, how many potential outcomes are there?
7 26. How many potential combinations can be made from a lottery ticket with four digits, the first two digits being any letter from the alphabet and the last two being any number Explain the difference between dependent and independent events. 28. If we remove all the kings and queens from a 52 card deck, how many unique four card sequences can we draw? 29. What classifies a permutation? 30. How many three digit permutations can be made from the numbers 1, 2, 3, 4, and 5 if repetition is not allowed? 31. How many three digit permutations can be made from the numbers 1, 2, 3, 4, and 5 if repetition is allowed?
8 32. How many possible codes can be formed with a locker that asks for four numbers, numbers cannot be used more than once, and any number can be 09? 33. What classifies a combination? 34. How many combinations without repetition are possible if we have four initial choices for three decisions? 35. How many combinations with repetition are possible if we have four initial choices for three decisions? 36. If Becca is at the store and can buy any three fruit (the store sells apples, oranges, pears, bananas, and kiwis), how many combinations of fruit can she choose?
9 37. Given the same number of elements and choices to make, which will there be more of: permutations or combinations? Why? 38. If we want to make a five letter word using any letters in the alphabet, how many possible words can we make (a word counts as any sequence of letters in this case)? Feel free to leave your answer in exponential or factorial form. 39. How many sandwiches can we make with one slice of turkey, one slice of ham, one slice of cheese, one dollop of mayonnaise, one dollop of ketchup, and one dollop of mustard if we are only using four ingredients? 40. How many sandwiches can we make with access to unlimited turkey, ham, cheese, mayonnaise, ketchup, and mustard if we are only using four ingredients?
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