WIR Math 166-copyright Joe Kahlig, 09C Page 1Week in Review #2Section 1.2: The number of elements in a Set.• n(A) denotes the number of things in set A.• n(φ) = 0• Set A and B are disjoint provided that A ∩ B = φ• A and B are any two sets.• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)• A, B, and C are any three sets.• n(A ∪ B ∪ C) = n(A) + n(B) + n(c) − n (A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C)1. If n(A ∩ Bc) = 75, n(Bc) = 155, n(Ac) = 95, and n(U ) = 190, what is n(A ∪ B)?2. A group of 160 students were asked which of these sports they participated in high school.15 students participated in all of these sports25 students participated in basketball and track.25 students participated in basketball and Tennis b ut not track.15 students participated in track but not tenn is.70 students participated in basketball.100 students did not participate in tennis.37 students participated in exactly one sport.(a) Fill in the Venn diagram.(b) How many students participated in track?(c) How many stu dents participated in at least two sports?(d) How many students participated in basketball or tennis but did not participate in track?WIR Math 166-copyright Joe Kahlig, 09C Page 23. A group of students were asked which of these types of pets: dogs, cats, or fish, they had when theywere kids.28 said they only had a dog.6 said they had all three of these pets.16 said they had a dog and a fish.15 said they had a fish but did not have a cat.48 said they only had one of these types of pets when they were a kid.57 said they had fish or a cat as a pet when they were a kid.87 said they did not have a fish as a pet when they were a kid.57 said they did not have a dog as a pet when they were a kid.(a) Fill in the Venn diagram.(b) How many students were in the survey?Section 1.3: Experiments, Sample Spaces, and Events.• An experiment is an activity with observable results.• Sample space, S, is the set consisting of all possible outcomes of an experiment.• An event is a subset of a sample space.• An elementary(or simple) event is an event with a single outcome.• The impossible event is the empty set• The certain event is the sample space.• The events E and F are mutually exclusive if E ∩ F = φ.4. Suppose a card is randomly dr awn from a standard deck of cards and the face value (denomination)is recorded. Find the sample space.5. An experiment consists of selecting a letter at random from the letters in th eword REPRESENTATIVE and observing the outcome.(a) Describe an appropriate sample space.(b) How many events does this sample s pace have?(c) Describe the event “the letter selected was a vowel”.WIR Math 166-copyright Joe Kahlig, 09C Page 36. An experiment consists of picking an integer from 0 to 10.(a) Describe an appropriate sample space.(b) Describe the event E that th e number picked was even.(c) Describe the event F that the number was a multiple of 3.(d) Describe the event G that the number was a multiple of 5.(e) Describe the event H that the number was odd and greater than 5.(f) Find the event FC∩ (H ∪ G).(g) Which pairs of event, E, F, G, and H are mutually exclusive?(h) If the number 6 was picked, which of the events E, F, G and H o ccur red?7. The numbers 0, 1, 2, 3, 4 are on separate pieces of p aper in a hat. Two p ieces of p aper are drawn atthe same time and the product of th e numbers is recorded. Find the sample space.WIR Math 166-copyright Joe Kahlig, 09C Page 48. Three quarters, four dimes and a nickel are in a piggy bank. Two coins are drawn at the same timeand the total dollar amount is recorded.(a) Find the sample space.(b) describe the event a quarter is drawn.(c) Describe the event the total is less than $0.33.Section 1.4: Basics of Probability• Probability is a nubmer assigned to each outcome in an experiment that indicateshow likely that ourcome is to occur with r espect to the other outcomes in the sample space.• empirical probability is probability based off of repeated trials of an experiment.• sometimes called relative frequency.• probability properties• 0 ≤ probability of any outcome(simple event) ≤ 1.• the sum of the probability of all of the ou tcomes is 1• a probability distribution is a chart that shows the outcomes and theprobability associated to each outcome.• For a uniform (equally likely) s ample space, each outcome will have the same probability,1n(S).• To find the probability of an event E, add the probabilities of all of the outcomes in the event.• Probability formulas• P (E ∪ F ) = P (E) + P (F ) − P (E ∩ F )• if E an d F are mutually exclusive then P (E ∩ F ) = 0• P (E) + P (EC) = 1 or P (E) = 1 − P (EC)9. An experiment consits of selecting a digit from the number 11112233444445556777777 and observingit. Give the probability distribution for this experiment.WIR Math 166-copyright Joe Kahlig, 09C Page 510. An experiment is to roll two 4 sided die(one red and one green) and record the product of the roll.Give the probab ility distribution for this experiment. Is the sample space uniform?11. A sample of 100 college students were asked their party affiliation and whether they favor state lotterymoney used for welfare.Favor Not Favor Unsure totalDemocrat 23 6 7 36Republican 14 25 4 43Independent 18 3 0 21total 83 34 11 100A person is selected at random f rom the sample. What is the probability the person(a) Does not favor the use of lottery money for welfare?(b) Is a Republican?(c) Is an Independent who is not sure?12. One card is selected from a standard deck of cards. What is the probability that the card is(a) a heart and a face card?(b) a heart or a f ace card?(c) not a club?(d) not a 4?WIR Math 166-copyright Joe Kahlig, 09C Page 613. A jar contains six red marbles numbered 1 to 6 and eleven purple marbles numbered 1 to 11. A marbleis drawn at random from the jar. Find the probability that(a) the marble is purple.(b) the marble is even.(c) the marble is pur ple or even.14. A fair coin is tossed three times and heads or tails is ob s erved after each flip. What is the probabilitythat(a) exactly one head is tossed?(b) at least two heads are