Use Venn diagrams to determine whether the following statements are equal for all sets A and B. 2) A' B', A B Answer: not equal

Transcription

1 Test Prep Name Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} Determine the following. ) (A' C) B' {r, t, v, w, x} Use Venn diagrams to determine whether the following statements are equal for all sets A and B. 2) A' B', A B not equal ) B (A C), (B A) (B C) equal ) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 00 responses with the following results: 90 were interested in an interview show and a documentary, but not reruns. 2 were interested in an interview show and reruns but not a documentary 2 were interested in reruns but not an interview show. 2 were interested in an interview show but not a documentary. 0 were interested in a documentary and reruns. 8 were interested in an interview show and reruns. 2 were interested in none of the three. How many are interested in exactly one kind of show? Find the requested angle. 5) Supplement of. 6.6

2 Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use =. when necessary. 6) 0 cm 0 cm 0 cm 6.6 cm Convert the following. ) yd to cubic feet. 89 ft Fill in the missing value. 8) 90,000 mm2 = cm ) 6.6 L = cm ) Find the volume of a cylinder with radius 6 cm and height 0 cm. Use. for. Round your answer to the nearest tenth. 0. cm Convert as indicated. ) 5 lb to grams g 2) 2.6 ft to centimeters 8 cm Find the probability. ) A bag contains balls numbered through. What is the probability of selecting a ball that has an even number? 8 2

3 ) One digit from the number,8,99 is written on each of seven cards. What is the probability of drawing a card that shows 9? 2 5) A fair die is rolled. What is the probability of rolling a or a? 6) A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a? ) One digit from the number,989,669 is written on each of seven cards. What is the probability of drawing a card that shows or 6? 8) A bag contains 8 red marbles, 2 blue marbles, and green marble. What is the probability of choosing a marble that is not blue? 9 9) The chart below gives the number of vehicle tags sold in each city. Find the odds. 20) City Number of Vehicle Tags Sold Bristol,86 Trevor 50 Camp Lake 2,5 Salem Paddock Lake 2,5 One car is selected at random from the cars with vehicle tags from these cities. What is the probability that this car is from Salem? (Round your answer to four decimal places.) 0.60 What are the odds in favor of spinning an A on this spinner? :5

4 2) A number cube labeled with numbers, 2,,, 5, and 6 is tossed. What are the odds in favor of the cube showing a? :5 22) The odds against Muffy beating her friend in a round of golf are : 8. Find the probability that Muffy will lose. 9 2) The odds in favor of a horse winning a race are posted as 9 :. Find the probability that the horse will win the race. 9 2) The chart shows winnings for, in dollars, for the 0 highest-rated FASTCAR drivers for last driving season. Driver Winnings Rick Bobby $6,0,66 Maverick St. Joseph $5,98,600 Johnny Wright $2,0,8 Jay Smith $,0,656 William Rock $2,95,95 Bob Ricky $,020,08 Jimmy Novak $,20,069 Tommy Keefe $5,50,50 Tyler Jones $,9,5 If one of the drivers listed in the chart is selected at random, determine the odds against the driver earning more than $6 million last season. 8 : Use the counting principle to obtain the answer. 25) The frequency setting for a garage door opener is determined by the positions of ten switches, each of which can be set to a "+" or "-" position. In how many ways can the switches be set? 02 26) A restaurant offered salads with 5 types of dressings and 6 different toppings. How many different types of salads could be offered? 0 2) There are balls in a hat; one with the number 2 on it, one with the number on it, and one with the number 9 on it. You pick a ball from the hat at random and then you flip a coin. Using a tree diagram, obtain the sample space for the experiment. List the elements that make up the sample space. 2 H, 2 T, H, T, 9 H, 9 T

5 28) There are balls in a hat; one with the number on it, one with the number 2 on it, and one with the number 5 on it. You pick a ball from the hat at random and then you roll a die. Using a tree diagram, obtain the sample space for the experiment. Then, find the probability that the number on the ball is greater than the number on the die ) There are cards in a hat; one is a king, one is a queen, and one is an ace. Two cards are to be selected at random with replacement. Using a tree diagram, obtain the sample space for the experiment. Then, find the probability that you choose the same card twice. Find the probability. 0) Each of ten tickets is marked with a different number from to 0 and put in a box. If you draw a ticket from the box, what is the probability that you will draw 2, 5, or? 0 ) A single die is rolled one time. Find the probability of rolling an odd number or a number less than. 2 2) One card is selected from a deck of cards. Find the probability of selecting a red card or a card less than. (Note: The ace is considered a low card.) 9 26 ) A survey of senior citizens at a doctor's office shows that 0% take blood pressure-lowering medication, % take cholesterol-lowering medication, and % take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication? 0. ) A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a red card? 8 Find the probability. 5) If 82% of scheduled flights actually take place and cancellations are independent events, what is the probability that separate flights will take place? ) If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second. 6 5

6 ) A family has five children. The probability of having a girl is /2. What is the probability of having no girls? 0.0 8) Elise has put 5 cans (all of the same size) on her kitchen counter; 2 cans of vegetables, 2 cans of soup, and can of peaches. Her son, Ryan, takes the labels off the cans and throws them away. Elise then chooses 2 cans (without replacement) at random to open. Find the probability that she will open at least can of soup. 0 9) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen. 66 0) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd. ) If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade. Two marbles are drawn without replacement from a box with white, 2 green, 2 red, and blue marble. Find the probability. 2) The second marble is red given the first marble is white. 2 ) The second marble is white given the first marble is blue. Use the table to find the probability. ) The table shows the number of college students who prefer a given pizza topping. toppings freshman sophomore junior senior cheese meat veggie Determine the probability a student prefers meat topping given that student is junior

7 5) The following table indicates the preference for different types of soft drinks by three age groups. cola root beer lemon-lime under 2 years of age between 2 and over 0 years of age If a person is selected at random, find the probability that the person is over 0 and drinks cola. 5 Evaluate the expression. 6) P 6,25,520 ) How many 5-digit numbers can be formed using the digits 0,, 2,,, 5, 6,, 8, 9, if repetitions of digits are allowed? 00,000 five-digit numbers 8) In how many ways can people be chosen and arranged in a straight line, if there are people from whom to choose? 80 ways An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. 9) In how many ways can the awards be presented so that Maria and Olivia will be next to each other?,0 50) A license plate is to consist of 2 letters followed by 5 digits. Determine the number of different license plates possible if repetition of letters and numbers is permitted. 6,600,000 5) How many ways can the letters in the word "WISCONSIN" be arranged? 5,60 Evaluate the expression. 52) 6 C 6 5) C P 2 5) How many ways can a committee of 2 be selected from a club with 2 members? 66

8 55) In how many ways can a group of 9 students be selected from 0 students? 0 56) Bob is planning to pack 6 shirts and pairs of pants for a trip. If he has shirts and pairs of pants to choose from, in how many different ways can this be done? 60,060 5) If you toss five fair coins, in how many ways can you obtain at least one head? 58) The chorus has six sopranos and eight baritones. In how many ways can the director choose a quartet that contains at least one soprano? 9 Find the probability (as a decimal rounded to four decimal places). 59) A bag contains 6 cherry, orange, and 2 lemon candies. You reach in and take pieces of candy at random. Find the probability that you have all cherry candies ) A bag contains 6 cherry, orange, and 2 lemon candies. You reach in and take pieces of candy at random. What is the probability that you have at least 2 orange candies?