Math 1 Unit 4 Mid-Unit Review Chances of Winning

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1 Math 1 Unit 4 Mid-Unit Review Chances of Winning Name My child studied for the Unit 4 Mid-Unit Test. I am aware that tests are worth 40% of my child s grade. Parent Signature MM1D1 a. Apply the addition and multiplication principles of counting. 1. Jessica is going shopping to buy a new outfit. At the store, she had 4 shirts to choose from, 5 brands of jeans, and 5 pairs of shoes. How many different outfits can she buy? 2. At Subway, you have 6 sandwiches to choose from, 4 bags of chips, 3 types of cookies, and 8 drinks. You want a sandwich, chips, and drink OR you want a cookie and a drink. Find the number of combinations possible. 3. Kierra has 4 pennies and two 6-sided number cubes. a) What is the total number of possible outcomes if Kierra flips all 4 pennies or rolls both number cubes? b) What is the total number of possible outcomes if Kierra flips all 4 pennies and rolls both number cubes? 4. You decide to lock your phone so no one can read your text messages. Using any 4 digits, how many passwords can you make using any number 0 9? (Digits can be used more than once.) 5. To the right are the types of crust and toppings offered at Papa John's Pizza. How many different ways could a customer order one type of crust and one topping? Type of Crust thick crust thin crust Toppings pepperoni hamburger onions pineapple 6. A.J. is creating a sandwich. He has three choices of meat (ham, turkey, or chicken) and four types of bread (wheat, white, French, or sourdough). If he randomly selects a meat and a type of bread, what is the probability that he will have a turkey sandwich? MM1D1 b. Calculate and use simple permutations and combinations. Formula for Permutations: Formula for Combinations: C P P C How many ways can you rearrange the letters in the word TUESDAY? 12. Find the number of ways you can arrange 3 letters of the word DANGER. 13. Libby, Josh, Trey, David, and Jacob are in line for lunch. How many different ways could they be ordered? 14. You need a password for your Facebook account. The password needs to have 5 characters. The first three must be letters and the last two must be numbers (0-9). How many different passwords are possible if you cannot use a letter or number more than once?

2 15. A box contains 8 tiles, each a different color. Sally is going to select 2 tiles without replacement. How many different groups of 2 differently- colored tiles could Sally choose? 16. A club consists of 6 girls and 8 boys. They must choose 2 boys and 2 girls to represent them in the school's parade. In how many ways can the club be represented? 17. Eight people are competing in the 100-yard dash. How many arrangements of first, second, and third place winners are possible? 18. There are 14 songs that you want to put on your mp3 player, but you can only fit 7 more songs. How many different groups of 7 songs can you choose? MM1D2 a. Find the probabilities of mutually exclusive and overlapping events. 19. Use the spinner on the right to answer the questions below. a) What is the probability that you will win $1000 on your first spin? b) What is the probability that you will win less than $500 on your first spin? c) What is the probability that you will land on either the $300 or a space greater than $600? 20. You have a bag of 10 green markers, 4 blue markers, 8 red markers, and 2 brown markers. You randomly select a marker out of the bag. a) What is the probability the marker will be blue? b) What is the probability the marker will be green or brown? c) What is the probability the marker will NOT be brown? d) Find P(red or blue). 21. If you draw one card from a standard deck of 52 cards, find each of the following: a) a red face card b) a number 6 c) P(9 or King) d)p(ace or heart) 22. Nadia will flip a fair coin. What is the probability that the coin will land on either heads or tails? 23. The gender and year distribution for a class are found below. If one student is randomly selected, what is the probability that the student will be a female or a senior? Male Female Junior 5 4 Senior 12 8

3 MM1D2 b. Find the probabilities of independent and dependent events. 24. If Danny randomly selects a card from a standard 52 card deck, a) what is the probability that he will choose a Jack and then a 10, without replacement? b) what is the probability of drawing a 7, not replacing it, and then drawing a Queen? c) what is the probability of drawing a 7, replacing it, and then drawing a Queen? 25. The letters of the word MISSISSIPPI are each written on a card. Find each of the following probabilities assuming that you pick one card, do not replace it, and then pick another card. a) P(M, then I) b) P(I, then I) c) P(S, then not S) d) P(S, then I) 26. A bag contains 2 red marbles, 3 blue marbles and 4 green marbles. A marble is randomly chosen, its color noted, and then it is put back. Then another marble is chosen. a) What is the probability of drawing one green and one blue? b) What is the probability of drawing two red marbles? c) What is the probability of drawing a red, a blue, and then a green? 27. In a class of 7 boys and 10 girls what is the probability of choosing a girl from the class and then choosing a boy from the remaining students? MM1D2 c. Calculate conditional probabilities. 28. You randomly choose 2 cards from a deck. Given that the first card is a 9, what is the probability that the second card is a Queen? 29. You will draw 4 cards from a deck without replacement. What is the probability that all 4 cards will be 8's, if you know that the first card was an 8? 30. You toss 3 coins. What is the probability that all 3 tosses will result in heads, if you know that the first toss resulted in heads? 31. A certain medical procedure has a 65% success rate. a) If the procedure is done twice, what is the probability that it will fail both times? b) What is the probability that it will be fail the first time and be successful the second time?

4 32. The question "Did you vote in the last Presidential Election?" was asked to 100 people. a) What is the probability that a randomly selected individual is a male? b) What is the probability that a randomly selected female did not vote? c) What is the probability that a randomly selected person who did vote is a male? Yes No Total Male Female Total The probability that it is Friday and that a student is absent is Since there are 5 days in a school week, the probability that it is Friday is 0.2. What is the probability that a student is absent if it is Friday? 34. At a high school, 32% of all students play football and 18% of all students play football and basketball. What is the probability that a student plays basketball given that the student plays football? people were randomly surveyed on their level of education. The data is below. High School 2 year college degree 4 year college degree 5 year college degree (Associates) (Bachelors) (Masters) Male Female a) What is the probability that the randomly selected person has a Masters degree? b) If you knew that the person interviewed was female, what is the probability that the person has a Bachelors degree? c) If you knew that the student interviewed was a male or female, what is the probability that the person did not have a college degree? d) If the randomly selected person has an Associates degree, what is the probability that the person is a male? e) If you knew that the student did not have a Masters degree, what is the probability that the person was not a male? MM1D2 d. Use expected value to predict outcomes Outcome Value, x Probability, p 1/4 1/5 1/20 1/2 Outcome Value, x Probability, p Family size and the probability of that size family in a certain neighborhood are represented in the table below. What is the expected family size in this neighborhood? Family Size Probability 18% 44% 25% 13%

5 39. June likes to run with her IPOD so she doesn t get bored. If she has her ipod she can run 4 miles on the treadmill before she gets bored, but she can only run 1 mile on the treadmill without her ipod. If she remembers to take her ipod to the gym 80% of the time, how many miles can she expect to run? 40. There is a prize drawing for home electronics. Tickets are $8. There are a total of 5000 tickets sold for the drawing. The three prizes are a new computer worth $1500, a high-definition TV worth $800, and an ipod worth $200. If you buy one ticket, what is the expected value of your gain/loss? 41. Use the spinner on the right to answer the questions below. a) Find the expected value if you spin the spinner once. b) What is the expected value if you spin the spinner twice? c) If you paid $3 to spin this wheel, how much should you expect to gain/lose on average? 42. Ryan puts 2 nickels, 2 dimes, and 1 quarter in a bag. He then picks one coin at random. What is the expected value, in cents, of each pick in this experiment?