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Unit 4 Study Guide 1. The school's new computer network requires each user to create a password. How many passwords are possible if each of the following restrictions are imposed? A) The password is four characters long and each character must be a digit (0-9)? B) The password is four characters long and starts with a letter followed by three digits (0-9)? 2. Find the number of choices you have for a hot beverage at a local coffee shop if you can choose one of 11 different espresso drinks or 5 different varieties of tea? 3. How many ways can a team of 5 players be selected from a roster of 11 players? 4. How many ways can first through fifth place be awarded in a race with 11 competitors (no ties)? 5. How many two-character codes exist that start with one of the 11 letters A-K and end with one of the 5 digits 0-4? 6. The math department at a high school has 9 teachers: 6 females and 3 males. Three of the teachers will be randomly selected to go to a math conference. A) How many groups of three teachers are possible? lions (@ B) How many groups of three teachers are all female? C) What is the probability that all of the teachers randomly selected are female? awow 7. What's the probability that a 5-card poker hand contains no hearts? Prob &8 . What's the probability that a 5-card poker hand contains 3 spades, 1 diamond and 1 clubs? 9 . Define each term below and give an example of two events that meet these criteria. A) Mutually Exclusive (Disjoint) B) Independent 10. What do you need to check to decide if a probability assignment is valid? 11. At a STEM convention, there are 7 math instructors, 5 science instructors, 3 educational technology instructors, and 4 engineering instructors. If an instructor is selected, find the probability of selecting a science or math instructor. 12. In a science class, there are 18 juniors and 10 seniors. 6 of the seniors are females and 12 of the juniors are males. If a student is selected at random, find the probability of selecting a junior or a female. 13. 85% of cars brought to Sam's Garage need an oil change, 17% need air in the tires, and 12% need both. What is the probability that a randomly selected car needs C) an oil change or air in the tires. D) an oil change, but does not need air added to the tires. Folemol lig sis cod E) neither an oil change nor air in the tires. 14. Two cards are drawn from a deck with replacement. What is the probability of drawing a spade and then drawing an ace? 15. Three cards are drawn from a deck without replacement. What is the probability of drawing a jack, an ace, and then another jack?16. A study found that 72% of people wear seat belts. If three people are selected at random, find the probability that F ) all three wear their seat belts . G) none of them wear their seat belts . H) at least one person wears their seat belt. 17. A bag contains 8 blue chips, 7 green chips, and 2 white chips. If three chips are drawn without replacement, what is the probability of drawing two blue chips and then a green chip? 18. Approximately 9.5% of the MVHS student body takes Probability & Statistics from Ms. Greenwald. According to the student survey conducted at the beginning of the year 75.7% of Ms. Greenwald's students plan to go to college after high school. What is the probability that a randomly selected MVHS student takes Prob & Stats from Ms. Greenwald and plans to go to college? 19. The table below represents the medal distribution from a world competition. If one medal winner is selected at random, find the following probability that Gold Silver Bronze Total A) they won a gold medal. United States 103 Russia 92 B) they a gold medal winner from the United States. china 14 Australia 16 49 Total 111 99 97 307 C) they won a gold medal given that they are on the US team. 20. An airport screens bags for forbidden items, and an alarm is supposed to be triggered when a forbidden item is detected. Suppose that 5% of bags contain forbidden items. If a bag contains a forbidden item, there is a 98% chance that it triggers the alarm. If a bag doesn't contain a forbidden item, there is an 8% chance that it triggers the alarm. A) Draw a tree diagram that includes the probabilities for all possible outcomes. B) What is the probability that a randomly selected bag does not contain a forbidden item and sets off the alarm? Prob & StaC) Given a randomly chosen bag contains a forbidden item, what is the probability that it does NOT set off the alar art now modt to ston ( D) What is the probability that a randomly selected bag sets off the alarm? 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