Counting Outcomes. Finding the probability that event A AND event B occur

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1 Name: Block: Date: UNIT (6) PROBABILITY SUBJ Algebra SKILL (6) Finding the probability that event A OR event B occurs. NOTES Counting Outcomes For extra practice, see Text Lessons 10.7 Counting Principle vs. Permutations vs. Combinations T/F. There are 3 True/False questions on Josh s science quiz. How many different ways can the questions be answered? AM. You are taking 6 classes, three before lunch. How many possible arrangements are there for your morning classes? D1. There are 21 girls on a Division I soccer team. Two will be picked to be on the All-American Team. How many different groups of players can be chosen? Finding the probability that event A AND event B occur Independent Events vs. Dependent Events First Outcome DOES NOT AFFECT Second Outcome First Outcome AFFECTS Second Outcome P(A and B) = P(A) P(B) P(A and B) = P(A) P(B given A) 1 & 1. A basketball player s has an 82% freethrow percentage. As a percent rounded to the nearest whole, what is the probability that the player will make his next two free throws? PB. A variety box of granola bars contains: 5 oats n honey, 3 peanut butter, and 4 cinnamon bars. If you pick two bars without looking, what is the probability that both will be peanut butter? Report your answer as a fraction.

2 U(6) S(6) p. 2 Finding the probability that event A OR event B occurs Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.1): A number cube is rolled. As a fraction, what is the probability that a 2 or an odd number is rolled? Ex. (O.1): You roll two number cubes. As a fraction, what is the probability that you roll a number less than 5 or an even number? P(2) P(odd #) P(# < 5) P(even #)

3 U(6) S(6) p. 3 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.2): A number cube is rolled. As a fraction, what is the probability that you roll an even number or a 5? Ex. (O.2): You roll two number cubes. As a fraction, what is the probability that an odd number or a 1 is rolled? P(even #) P(5) P(odd #) P(1)

4 U(6) S(6) p. 4 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.3): A black number cube is rolled. As a fraction, what is the probability that you roll a multiple of three or a 5? Ex. (O.3): A number cube is rolled. As a fraction, what is the probability that you roll a multiple of three or a 6?

5 U(6) S(6) p. 5 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.4): A black number cube is rolled. As a fraction, what is the probability that you roll a multiple of two or a 3? Ex. (O.4): You roll two number cubes, one black and. What is the probability that you roll a 4 on one of the cubes? Express your answer as a percent rounded to the nearest whole. 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6,

6 U(6) S(6) p. 6 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.5): A black number cube is rolled. As a fraction, what is the probability that you roll an even number or a 1? Ex. (O.5): You roll two number cubes, one black and. What is the probability that you roll a 5 or a 6 on one of the number cubes? Express your answer as a percent rounded to the nearest whole. 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6,

7 U(6) S(6) p. 7 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.6): A black number cube is rolled. As a fraction, what is the probability that you roll a number less than 4 or greater than 5? Ex. (O.6): You roll two number cubes, one black and. What is the probability that you roll a 1 or a 2 on one of the number cubes? Express your answer as a percent rounded to the nearest whole.

8 U(6) S(6) p. 8 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.7): Eight $100 raffle tickets are sold for the chance of winning a week-long cruise to Bermuda. One ticket will be randomly chosen as the wining ticket. Say you buy 2 tickets, and your friend buys 3 tickets. As a fraction, what is the probability that you or your friend wins the raffle? Ex. (O.7): Ten $200 raffle tickets are sold for the chance of receiving a batting lesson from Yankee great Derek Jeter. One ticket will be randomly chosen as the wining ticket. Two tickets are sold to sixth grade boys, three tickets are sold to sixth grade girls, one ticket is sold to a fifth grade boy, and four tickets are sold to fifth grade girls. As a fraction, what is the probability that a sixth grader or a girl wins the raffle? P(you win) P(friend wins) P(6 th Grader Wins) P(girl wins) X X X 2 X X 2 X X 2 X X 6B 6G 5G 6B 6G 5G 6B 6G 5G 6B 6G 5G 5B

9 U(6) S(6) p. 9 Disjoint Events vs. Overlapping Events Two events have NO OUTCOMES IN COMMON P(A or B) = P(A) + P(B) Two events have OUTCOMES IN COMMON P(A or B) = P(A) + P(B) P(AB) Ex. (D.8): Two girls lacrosse players, 3 girls basketball players, 4 boys basketball players, and 1 boys lacrosse player are all playing a pick-up game of basketball after school. As a percent, what is the probability that a girls lacrosse player or a boys lacrosse player will be on a team? Ex. (O.8): Two girls lacrosse players, 3 girls basketball players, 4 boys basketball players, and 1 boys lacrosse player are all playing a pick-up game of basketball after school. As a percent, what is the probability that a girl or a lacrosse player will be on a team? P(girls lax) P(boys lax) P(girl) P(lax player) GB GB GB GL GL BL BB BB BB BB GB GL BL GB GL 5G GB 6G 5G 6B 6G 5G BB BB BB BB

10 U(6) S(6) p. 10 Concept Checks with Disjoint Events and Overlapping Events DIRECTIONS for (1) (5): Before solving the problem, tell whether the question is asking you to find a: P(Disjoint Event) P(Overlapping Event) P(Independent Event) P(Dependent Event). For (1): Rolling more dice A) What is the probability of rolling a three or an even number? Report your answer as a fraction and as a percent rounded to the nearest whole. B) Find the probability of rolling an even number or a number greater than 3. Report your answer as a fraction and as a percent rounded to the nearest whole. C) Find the chances of rolling an even number or a prime number. Report your answer as a fraction and as a percent rounded to the nearest whole. D) What is the probability of rolling a number less than 4 or an even number? Report your answer as a fraction and as a percent rounded to the nearest whole. E) If two dice are rolled, what is the probability of getting one 6? Report your answer as a fraction and as a percent rounded to the nearest whole. F) What are the chances of rolling doubles when you roll two dice? Report your answer as a fraction and as a percent rounded to the nearest whole. For (2): Dressing some salads The list below shows types of salad dressings made by Kraft. A) If you send your cousin to the store to pick up a Kraft salad dressing for dinner tonight, what is the probability that your cousin will bring back a bottle of Kraft s Creamy French or Bleu Cheese? Report your answer as a fraction and as a percent rounded to the nearest whole. B) You hear that there will be a coupon in this Sunday s newspaper for one of the flavors of Kraft s salad dressing shown to the right. What is the probability that the coupon will be for a flavor of Kraft s dressing that has the words light or fat free in it? Report your answer as a percent rounded to the nearest whole. C) Harris is sent to the store by his wife to pick up a bottle of Kraft s salad dressing. What is the probability that Harris will bring back a bottle of fat-free dressing or one of the many ranch flavors Kraft offers? Report your answer as percent rounded to the nearest whole. D) If Ronnie is sent to the store by his wife to pick up a bottle of Kraft s salad dressing, find the probability that he purchases one of the Thousand-Island flavors or a bottle that contains a bacon flavor. Report your answer as a percent rounded to the nearest whole. Kraft Salad Dressings Bleu Cheese Caesar, with Bacon Caesar Catalina Catalina, Fat Free French, Creamy Honey Mustard Italian Italian, Fat Free Ranch Ranch, Fat Free Ranch, with Bacon Ranch, Buttermilk Thousand Island Thousand Island, with Bacon Vinaigrette, Balsamic Vinaigrette, Light Raspberry

For (3): College GameDay. College GameDay is an ESPN entertainment show previewing college basketball games. The show is taped at a different college each week.

Suppose the College GameDay show took place last weekend at Duke University. In the stands there were 432 male students and 168 female students.

11 For (3): College GameDay. College GameDay is an ESPN entertainment show previewing college basketball games. The show is taped at a different college each week. During each show, one student is chosen at random from the stands to attempt a half-court shot in hopes of winning a check for $18,000 from State Farm Insurance. Suppose the College GameDay show took place last weekend at Duke University. In the stands there were 432 male students and 168 female students. Amongst these students, there were: 18 men s soccer players; 12 men s volleyball players; 22 women s soccer players; 11 women s volleyball players; and 8 women s softball players. As a percent rounded to the nearest whole: U(6) S(6) p. 11 (FYI: The $18,000 check from State Farm awarded to students who nail a halfcourt shot at an ESPN College Gameday show represents the 18,000 State Farm insurance agents who work across the country.) A) What were the chances that a soccer player or a volleyball player was chosen to attempt the half-court shot? B) Find the probability that a men s soccer player or a women s soccer player was the lucky person to take a chance at winning the $18 grand. C) Find the probability that a girl or a volleyball player was chosen to take the half-court shot. D) What was the likelihood that a guy or a soccer player was chosen to take the half-court shot? For (4): So far this basketball season, there have been 18 College Gameday shows, and only 2 students have hit the half-court shot. As a percent rounded to the nearest whole: A) Find the likelihood that the next person to attempt a half-court shot at a College Gameday show will make the shot. B) Based on the probability you calculated in part (A), what are the chances that a student will make a half-court shot at two out of the next three College Gameday shows? For (5): Every spring, college students are assigned their dorm rooms that they will be living in for the next school year. Suppose there is a new dorm building on campus at the University of North Carolina at Chapel Hill. Each room in the building is a single, meaning that one person lives in each room. FRESHMEN 4,299 Male 1,794 Female 2,505 SOPHOMORES 3,938 Male 1,668 Female 2,270 JUNIORS 4,475 Male 1,813 Female 2,662 At the time the university is assigning next year s living arrangements, the university has the enrollment shown to the left. As a percent rounded to the nearest tenth: A) What is the probability that a sophomore or junior will be assigned a room in the new dorm building? B) Find the probability that a male or a freshman student will receive a room in the new dorm building. C) What are the chances that a female or a junior will receive a new room? D) Find the likelihood that a freshman male or a freshman female gets a room. E) Ladies first! Find the probability that the first room assigned in the new dorm building goes to a female junior; the second to a female sophomore; and the third to a female freshman.

12 U(6) S(6) p. 12 Practicing w/ ALL the types of Probability problems now w/ Poker! DIRECTIONS for (6) (22): Before solving the problem, tell whether the question is asking you to find a: FIRST, tell whether the question is asking you to find a: Counting Principle P(Simple Event) P(Independent Event) P(Disjoint Event) Permutation P(Dependent Event) P(Overlapping Event) Combination SECOND, solve the problem. 6) Ducks. The lowest ranking card in poker is a two, known as a duck. As a fraction and as a percent rounded to the nearest whole, find the probability of picking a duck from a full deck of cards. 7) Hooks. A jack in the game of poker is called a hook. What is the probability of picking two hooks in a row from a full deck of cards if you do not replace the first card you pick? Report your answer as a percent rounded to the nearest tenth. POKER HAND RANKINGS, from strongest to the weakest: ROYAL FLUSH A ten, jack, queen, king, and ace, all of the same suit STRAIGHT FLUSH 8) Q/J. As a fraction and as a percent rounded to the nearest whole, what is the probability of picking a queen or a jack from a full deck of cards? 9) Q/. Find the probability of picking a queen or a diamond from a full deck of cards. Express your answer as a percent rounded to the nearest whole. 10) 5/. Calculate the chances of selecting a 5 or a spade from a full deck of cards. Report your answer as a percent rounded to the nearest whole. 11) Being dealt your hand: In the game of poker, players are dealt five cards from a standard deck of cards. Say you are playing poker with some of your buddies. If you are the first one to be dealt your five cards, how many different combinations of cards could you be dealt? 12) Holding your hand: After receiving your five cards, how many different ways could you order the cards in your hand? 13) The highest-ranking hand: The highest ranking hand in the game of poker is the royal flush. It consists of the following cards: a ten, a jack, a queen, a king, and an ace, all of the same suit (i.e. all hearts). Find the likelihood of being dealt a royal flush if you are the first person being dealt your five cards in a game of poker. Express your answer as a fraction. Five cards in sequence, all of the same suit FOUR OF A KIND Four cards of the same denomination, one in each suit FULL HOUSE Three cards of one denomination and two cards of another denomination FLUSH Five cards all of the same suit STRAIGHT Five cards in sequence of any suit THREE OF A KIND Three cards of the same denomination

14) Big Slick. The ace is the highest ranking card in poker and is referred to as the bullet. The next highest ranking card is the king and it is called the cowboy.

13 If Troy is being dealt his five cards first in a game of poker, find the probability that the first two cards dealt to Troy are an ace and a king.

13 14) Big Slick. The ace is the highest ranking card in poker and is referred to as the bullet. The next highest ranking card is the king and it is called the cowboy. If you have an ace and a king amongst your five cards, no matter what their suit (i.e. ace of hearts and a king of clubs) the ace and the king together are referred to as a big slick. U(6) S(6) p. 13 If Troy is being dealt his five cards first in a game of poker, find the probability that the first two cards dealt to Troy are an ace and a king. Report your answer as a percent rounded to the nearest whole. For (15): Your Place! You have 10 friends who enjoy playing poker. The poker table in your basement though only has enough room for seven players. A) If you are going to hold a poker night at your house on Friday, how many ways could you invite over your house a group of 6 of your friends who enjoy playing poker? B) When you and your six friends sit down at your poker table, how many different ways could you arrange yourselves around the table? For (16): Pizza Run! Halfway through your poker night, you and your six friends become hungry. A) How many ways could two of you be chosen to go to Sorrento s pizzeria to pick up a pizza pie? B) Your two friends Gale and Cory are chosen to go to Sorrento s. At Sorrento s they can order a small, medium, or large pizza pie made with a thin or regular crust; topped with one of the following choices: bacon; mushrooms; onions; pepperoni; or sausage. How many different ways could you place an order for a pizza pie from Sorrento s? C) You are not a fan of mushrooms or onions on your pizza. What is the probability that your friends will bring back a pie with mushrooms or onions on top? Report your answer as a fraction. D) What is the complement to the event you calculated in part (C)? Report your answer as a fraction. For (17): Use the data in the table to the right. It shows the results of a national survey conducted by Zagat in June A) Find the probability that the next three pizzas ordered at Sorrento s have pepperoni as a topping. Report your answer as a percent rounded to the nearest whole. B) What is the probability that one of the next three pizzas ordered at Sorrento s has onions as a topping? Report your answer as a percent rounded to the nearest whole. C) If there are 12 people dining in Sorrento s, how many would you expect to be eating their pizza by folding it? Round your answer to the nearest whole. D) When you and your six friends begin to eat the pizza you had ordered from Sorrento s, what are the chances that all six of your friends will eat their pizza by holding it flat? Report your answer as a percent rounded to the nearest whole percent. ZAGAT PIZZA SURVEY TOP 5 TOPPINGS Pepperoni 38% Mushrooms 37% Sausage 35% Onions 21% Ham/Prosciutto 15% HOW DO YOU EAT YOUR PIZZA? Eat it Flat 21:50 Fold it 19:50 Fork & knife 1:5

$Report each answer as a fraction and percent rounded to the nearest tenth: P(you win the next two games of poker) P(you lose the next two games of poker) P(you win one of the next two games of poker)$

14 U(6) S(6) p. 14 For (18): Winning Percentages in Poker. Out of the last 8 games of poker you played with your friends, you won two. A) Calculate your winning percentage; round it to the nearest tenth of a percent. B) Based on your winning percentage in part (A), find each probability below. Report each answer as a fraction and percent rounded to the nearest tenth: P(you win the next two games of poker) P(you lose the next two games of poker) P(you win one of the next two games of poker) Pop Quiz! What is the name of the hand shown to the right? For (19): Pick your Favorite Playing Card Game! Use the chart to the right to answer the questions below. A) As a percent rounded to the nearest tenth, find the experimental probability that a randomly chosen student from the survey would name poker as their favorite card game. B) If you randomly pick two students from the students who were surveyed, find each probability below. Express each answer as a percent rounded to the nearest tenth: P(both students named basic rummy as their favorite card game) P(only one of the two students you picked named basic rummy) Hey Middle Schoolers! What s your Favorite Card Game? No. of Responses Basic Rummy 26 Gin Rummy 21 Go Fish 14 Poker 6 Spades 7 C) Based on the results shown, find the probability that all three of your lab partners in science would name go fish as their favorite card game. Express your answer a percent rounded to the nearest tenth. D) What are the chances that your best friend would say either basic rummy or gin rummy was their favorite card game? Report your answer as a percent rounded to the nearest tenth. E) What is the likelihood that two out of the three students you sit with at lunch would name basic rummy as their favorite card game? Report your answer as a percent rounded to the nearest tenth. F) If Mendham Township Middle School has 124 sixth graders, about how many of these students would you predict would name spades as their favorite card game? Round your answer to the nearest whole. For (20): Poker for Parents! St. Therese School in Succasunna, NJ is holding a Casino Night this year to help raise money to purchase new technology for its students. A) At a normal casino, there are the following games to play: slot machines; poker; Black Jack; Ultimate Texas Hold em; Roulette; and Baccarat. If the organizers of the Casino Night at St. Therese School only have enough room to set up four of these games, how many ways could the organizers choose four different games to set up? B) Suppose the organizers choose the following four games to set up: slot machines; poker; Black Jack; and Ultimate Texas Hold em. If your parent attends Casino Night, how many combinations of three different games could your parent choose to play out of the four made set up? Make a tree diagram and a list to solve. C) When parents arrive at the Casino Night, each parent is randomly given one of the following: a card-game visor; a cup to collect the chips they win while playing card games; a poker key chain; or a pair of playing-card glasses. The probability of receiving a visor is 0.08 and a key chain If the probability of being given cup or a pair of glasses is the same, find the probability of being given a pair of glasses. Report your answer as a decimal.

15 For (21): The fast-moving rummy tile game! It is hard to find family games that are fun and challenging for both kids and adults, but Rummikub fills the bill on all counts. The object of Rummikub is similar to rummy card games: you need to combine your Rummikub tiles in runs (consecutive numbers in the same color) or sets (groups of the same number). All of the tiles to a Rummikub game are shown below (104 numbered tiles, and 2 joker tiles). At the beginning of the Rummikub game, each player randomly picks 14 of these tiles from a bag. U(6) S(6) p. 15 Say you are sitting down with three of your friends to play a game of Rummikub. You are the first person to randomly choose your 14 tiles from a bag filled with all of the tiles shown below. As a fraction and as a percent rounded to the nearest hundredth, find each probability below. Assume that each probability is being based on you first reaching into the full bag of tiles: A) P(picking a blue tile) G) P(picking an 11 or a black tile) B) P(picking the lucky number 7) H) P(picking a black joker and a red joker) C) P(picking a multiple of 4) I) P(picking a 1, then 2, then 3) D) P(picking a red 10 or an orange 10) J) P(picking the unlucky number 13 or a number greater than 10) E) P(picking an even number or a 1) K) P(picking a number less than 6 or an odd number) F) P(picking a blue tile or an 8) L) P(picking an even number and then an even number) Blue Red Orange Black ) Now! After you pick your 14 Rummikub tiles, how many different ways could you arrange them in a row on your tile board?

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LC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.

LC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply