Name: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11

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1 Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value trial occurrence. The possible outcome of an experiment is called a(n) trial occurrence outcome event. An experiment that models an actual event is a(n) trial simulation test experiment. A random variable's values tend toward a particular value. This value is called the median value expected value mean value average value. A simulation is conducted to determine the probability of a family having two girls and then a boy. This simulation could be done using a coin a deck of cards a die all of the above. An event occurs, on average, every out of 7 times during a simulation. The experimental probability of this event is A simulation is carried out to determine the experimental probability of being correct by guessing on five out of ten questions of a true/false test. The most time efficient simulation would be carried out using a coin a TI-8 Plus calculator a deck of cards all are equally time efficient 8. Drawing from a deck of cards is used to simulate answering a question correctly by guessing on a multiple choice question with four choices. In this simulation, the event of answering a question correctly would be drawing a spade drawing a heart or diamond drawing one of the four aces none of the above

2 . The chances of a family having a boy is simulated by tossing a coin ten times. Heads is used to simulate having a girl and tails is used to simulate having a boy. Out of ten trials, two heads and eight tails turn up. This experimental probability of 8 0 is close to the theoretical probability not close to the theoretical probability equal to the theoretical probability none of the above 0. Two friends play a game. They roll a die. If the roll is or, the first friend gives the second friend $.00. If the roll is a, the second friend gives the first friend $.00. The expected amount of money the first friend receives if the die is rolled times is $.00 $.00 $0.00 $.00. Two friends play a game. They roll a die. If the roll is or, the first friend gives the second friend $.00. If the roll is a, the second friend gives the first friend $.00. The amount of money the second friend receives, $0.00 or $.00, is called a(n) trial expected value simulation discrete random variable. A baseball player has a batting average of 0.. Using a TI-8 Plus calculator, the random integer command is used to simulate a batter at bat 0 times, to determine the number of hits made. The calculator screen should read randint(0,0,000) randint(,000,) randint(,000,0) randint(000,0,). Three percent of the lightbulbs that a company produces are defective. A simulation using a spreadsheet is conducted to determine the probability that four out of the next eleven lightbulbs produced are defective. This simulation is run a thousand times, with each row in the spreadsheet simulating a trial. The dimensions of the spreadsheet, including the trial number column, is 000 rows by columns rows by 000 columns rows by columns rows by columns. Three percent of the lightbulbs produced by a company are defective. A simulation using a spreadsheet is conducted to determine the probability that four out of the next eleven lightbulbs produced are defective. This simulation is run 8 times, with each row in the spreadsheet simulating a trial. The entries in the spreadsheet could be the numbers to 8 to 0 to 00 none of the above. The software program, Fathom, is used to generate random integers of the values,,, and. This could represent the simulation of a family having a boy or girl drawing a queen from a deck of cards determining if a batter with a batting average of 0. will have a hit determining if a product which is defective % of the time is defective. A bag contains red blocks, blue blocks, and yellow blocks. If you draw one single block, then n( S) is

3 7. The probability of drawing an ace out of a deck of cards is to be calculate The number of elements in the sample space is none of the above 8. The probability of rolling a number that is divisible by six with a single die is. Two dice are rolle The probability of rolling a sum less than is 0. The probability of drawing a face card from a deck of cards is. A spinner is divided into twelve equal sectors, numbered through. An event space is defined as spinning a number divisible by. The value of P(A ) is. The collection of all possible outcomes of an experiment is called the event space outcome space probability space sample space. A card is drawn from a regular deck of cards and a coin is flippe The probability of choosing the queen of hearts and turning up tails is to be determine The value of n( S) is 0 0. The theoretical probability of drawing a card that is black but not a face card is 0 8

4 . Each of the letters of the word PROBABILITY are placed in a hat. If one letter is drawn randomly, what is the probability that a vowel is pulled out? 8 7. A multi-sided die with less than 0 sides is rolle The probability of rolling a number divisible by is. The number of sides of the die must be 8 7. A student writes a multiple choice test that consists of questions, each with choices. What is the probability of the student have a perfect mark on the test by guessing? none of the above 8. A number between and 0 is randomly chosen.the probability of the number being a perfect square is 0 7 none of the above. Which of the following statements is true? n(a) n(s) n(a) = n(a ) P(A ) = + P(A) none of the above 0. In a hat, there are nickels and dimes. If two coins are chosen at random at the same time, the probability that both are nickels is. Two sets A and B are said to be disjoint if n( A B) = n( A) + n( B) n( A B) = n( A B) = n( A) = n( B) n( A B) =. Let set A be the set of even numbers between and 0. Let B be the set of all numbers divisible by three between and 0. Which statement is true? n(a B) = n(a B) = n(a B) = n(a B) =

5 . Let set A be the set of face cards and B be the set of all spades in a regular deck of cards. State which statement is true. n( A B) = n( A B) = n( A B) = n( A B) =. If A and B are mutually exclusive events, then P( A) + P( B) = P( A B) = P( A) + P( B) P( A B) = P( A) + P( B) P( A B) =. Which of the following is the additive principle for probabilities? P( A B) = P( A) + P( B) P( A B) P( A B) = P( A) + P( B) P( A B) P( A B) = P( A) + P( B) + P( A B) P( A B) = P( A) + P( B) + P( A B). Given that P( A) = 0., P( B) = 0., and P( A B) is 0., the value of P A B Ë Á The probability that John will be accepted into the business program at Probability College is 0.. The probability that he will be accepted into the science program is 0.. The probability that he will be accepted into both programs is 0.. What is the probability that he will be accepted into at least one of the programs? none of the above Ê ˆ is 8. Find the probability that when a single card is drawn from a regular deck of cards a diamond or six is chosen. 7 none of the above. At a high school, 8 students are enrolled in calculus, are enrolled in data management, and are enrolled in both subjects. How many students are taking calculus or data management? none of the above 0. In a high school of 000 students, are playing sports and are in a school ban If there are 7 students playing sports and are in a school band, how many are in neither activity? A bag contains marbles ( green and blue), and blocks ( green and blue). One object is drawn randomly. What is the probability that the object is a green marble or a block? 0 none of the above

6 . The probability that it will be sunny tomorrow is 0.. The probability that it will be sunny the day after is 0.. The probability that it will rain tomorrow and the next day is 0.. What is the probability that it will rain neither day? none of the above. On a particular night, 0% of a group of people polled say that they are going to watch the hockey game and 7% say they are going to watch both the hockey game and the news. If 87% say they are going to watch at least one program, what percentage of these people say they are going to watch the news? 7% % 0% none of the above. If P( A) = 0., P( A B) = 0. and P( A B) = 0., determine P( B) none of the above. The intersection of two sets is best associated with the word both or and none of the above Gender Mathematics English Males Females 7 8. A class is surveyed to determine whether they prefer mathematics or english. The table above shows the results. Given that a student is male, state the probability that mathematics is preferre none of the above 7. A class is surveyed to determine whether they prefer mathematics or english. The table above shows the results. State P(male prefers english). 7 none of the above 8. A class is surveyed to determine whether they prefer mathematics or english. The table above shows the results. State P(prefers english female) none of the above

7 . A bag contains nickels, dimes, and quarters. If a nickel is taken out and not replaced, state the probability that the next coin drawn will be a dime. none of the above 0. From a survey of 00 drivers, 00 drive cars, 0 drive SUVs, 0 drive minivans, and the rest drive trucks. Determine P(truck driver not a car driver). none of the above. Out of a group of 00 people, are adults and 7 are children. Of the adults, have brown eyes and of the children, have brown eyes. If a person is selected at random, determine the probability of that person being a child if the colour of eyes is known to be brown Out of a group of 00 people, are adults and 7 are children. Of the adults, have brown eyes and of the children, have brown eyes. If a person is selected at random, determine P(not having brown eyes adult) Determine the probability of drawing a spade and then a club from a regular deck of cards if the spade is not returned to the deck. 0. Determine the probability of drawing a face card and then an ace from a regular deck of cards if the face card is not returne 7

8 . A pair of students is picked randomly from four students John, Sara, Adam, and Laur Determine the probability that a girl will be chosen given that Adam has been chosen already.. A day is said to be rainy or not rainy. The probability of a rainy day tomorrow is 0.. The probability of it not being rainy on a day after a rainy day is 0.7. Determine the probability that the next two days will be rainy In a school, 70% of the students listen to musi Of those, 0% listen to rock music, 0% listen to dance music, and 0% listen to both types of musi Determine the probability that a student chosen at random listens to dance musi In a school, 70% of the sudents listen to musi Of those, 0% listen to rock music, 0% listen to dance music, and 0% listen to both types of musi Determine the probability that a student listens to music other than rock or dance music given that they listen to musi A study shows that a particular product will have problems in a ratio of one to ten. Of these problem products, 0% will be found in the first year and the rest after that. Determine the probability that a product will be found defective after one year Given the following Venn diagram, determine P( A B) none of the above 8

9 . Identify which situation represents two dependent events. drawing two cards from a deck without replacement flipping a coin twice rolling a pair of dice one after the other none of the above. The probability of being selected for committee A is 0.. The probability of being selected for committee B is 0.. If these are independent events, determine the chances of not being selected to either committee A three-digit code using the numbers to is given to a student at his high school. Determine the probability that the last two digits of the number are both. 8. An artist wins a prize 0% of the time when she enters an art show. Determine the probability that she will win exactly once out of two art shows A coin is flipped and a die rolle Determine the probability that the toss is heads and the roll is divisible by three. none of the above. A tennis player's first serve goes in 70% of the time. If he makes three serves, determine the probability of getting the second one in none of the above 7. Determine the number of ways that four objects can be chosen from a group of ten. P(0, ) C 0 0!! none of the above 8. The expression! is equivalent to!8! P(, ) C 8 the number of ways that out of can be arranged none of the above

10 Ê7ˆ. The expression is equivalent to Ë Á 7!! none of the above 70. From a group of seven junior and ten senior students, determine how many committees of six students can be chosen if all the students are senior students C(, 0) 7. From a group of seven junior and ten senior students, determine how many committees of six students can be chosen if four are junior students none of the above 7. From a group of seven junior and ten senior students, determine how many committees of six students can be chosen if at least one student is a senior student A bag contains four black marbles and nine orange marbles. If one marble is drawn randomly, determine the odds of pulling out an orange marble. : : 7. Determine the odds of drawing two aces if two cards are removed from a regular deck. : : :0 : 7. Three cards are drawn randomly from a hat containing cards with the twenty-six letters of the alphabet on them. Determine the probability of selecting A and B Determine the probability of choosing the jack and king of clubs out of a regular deck of cards when two cards are randomly chosen. 70 0

11 77. Determine the probability of choosing two hearts out of a regular deck of cards when two cards are randomly chosen There is a % of winning a prize in a particular contest. Determine the odds against winning a prize. :0 : 7: 7:0 7. The starting line up of a co-ed volleyball team must be made up of males and females. If the team has females and 8 males, determine the probability that Emma, Mary, and Brittany are selected for the line up A bag contains six blue marbles, seven red marbles, and four green marbles. If four marbles are drawn randomly, determine the probability that three are green Determine which of the following problems must be determined using a combination. Determine the probability of drawing an ace and a four from a deck of cards in that order. Determine the probability that Rhys, Lorne, Cheryl, and Carl are chosen when a group of six is chosen from nineteen people. Determine the probability of rolling doubles when a pair of dice are rolle Determine the number of ways that a captain and co-captain can be chosen from a football team of members. Short Answer 8. Determine the probability of drawing a red queen from a deck of cards. 8. A bag contains red marbles, blue marbles, black marbles, and yellow marbles. If a marble is drawn at random, determine the probability of not drawing a red marble. 8. A box contains balls with the numbers to 0 on it. One ball is drawn randomly. The probability of choosing a number divisible by is to be determine State the value of n( A). 8. A department store sells 00 tickets for a draw in which a set of furniture will be given away. One ticket is drawn at random. If an event space contains all tickets numbered 0 to, determine P(A ).

12 8. Two dice are rolle The probability of rolling doubles is to be determine State n(a ). 87. According to the following Venn diagram, what is the value of n(a B)? 88. According to the Venn diagram, state the value of P( B C). 8. According to the Venn diagram, state the value of n( A D). 0. Determine the value of P( B C D) from the diagram.. A group of people are asked about their music preferences. The number of people who say they like rock music is 8. The number who say they like country is 8. The number who say they like both types of music is. State the number of people who like rock or country musi. If a card is drawn randomly from a regular deck of cards, determine the probability that it is red or a face car. Two dice are rolle Determine the probability of rolling pairs or a sum of four.. Customers at a restaurant are surveyed to determine if they drink pop and eat ice cream. The probability of a person drinking pop determined to be 0.. The probability of a person drinking pop and eating ice cream is determined to be 0.. Determine the probability of a person eating ice cream given that they drink pop.. A prize bag has CDs, 7 video games, and DVD movies. Each winner picks one prize from the bag without looking in the bag. Determine the probability of the first two winners both choosing DVD movies as prizes.. A girls' phys-ed class is surveye The probability is determined that a girl who has played basketball and volleyball is 0.. Given that a girl has played basketball, the probability that she has played volleyball is 0.8. Determine the probability that a girl has played volleyball.

13 7. A group of bands performs at a music festival. Out of the bands, are from North America and 8 are not. Of the North American bands, 8 have signed with a label and have not. All but two of the bands not from North America have signed with a label. If a band is picked randomly, state the probability that the band is North American given that they have been signed to a label. 8. Determine C(, ).. Write C in terms of factorials. 00. Determine the number of ways that two flavours of ice cream can be chosen from 7 flavours. 0. A group of 0 children and adults are at a picnic, and are chosen randomly to win a prize. Determine the number of ways that two adults and three children can each win a prize. 0. A bag in a music class contains triangles, tambourines, and harmonicas. If instruments are drawn randomly, determine the number of ways that exactly of the are tambourines. 0. A bag in a music class contains triangles, tambourines, and harmonicas. If instruments are drawn randomly, determine the number of ways that at least of the instruments are triangles. 0. Determine the odds of rolling a sum of when a pair of dice are rolle 0. Determine the odds of a team winning a game if its percentage chance of winning is 7%.

14 Sample Mastery # Answer Section MULTIPLE CHOICE. B. D. C. C. D. D 7. C 8. A. A 0. B. D. B. A. B. A. D 7. A 8. A. A 0. D. B. A. D. C. C. B 7. B 8. D. A 0. C. C. D. A. B. A. C 7. A 8. C

15 . A 0. D. A. C. D. C. B. B 7. A 8. D. C 0. B. C. B. D. A. B. C 7. B 8. A. B 0. A. A. D. D. C. D. B 7. D 8. B. C 70. A 7. B 7. C 7. A 7. B 7. D 7. B 77. A 78. B 7. B 80. C

16 8. B SHORT ANSWER 8. The probability of drawing a red queen from a deck of cards is. 8. The probability of not drawing a red marble is. 8. The value of n(a) is. 8. The value of P(A ) is The value of n(a ) is The value of n(a B) is The value of P(B C) is. 8. The value of n(a D) is zero. 0. The value of P(B C D) is.. The number of people who like rock or country music is 0.. The probability that the card is red or a face card is 8.. The probability of rolling pairs or a sum of four is.. The probability of a person eating ice cream given that they drink pop is 0... The probability of the first two winners both choosing DVD movies is 0.. The probability that a girl has played volleyball is The probability that the band is North American is C(, ) is.. In terms of factorials, C is! 8!!. 00. There are ways. 0. There are 00 ways. 0. The number of ways is The number of ways is. 0. The odds of rolling a sum of is :8. 0. The odds are 7:.