12. Kiersten applies for admission to the University of Southern California (USC) and Florida State University (FSU). She estimates that she has a 60% chance of being admitted to USC, a 70% chance of being admitted to FSU, and a 35% chance of being admitted to both universities. (a) What is the probability that she will be admitted to either USC or FSU? (b) What is the probability that she will not be admitted to FSU? 13. A cooler contains 8 bottles of Pepsi®, 5 bottles of Coke®, 4 bottles of Mountain Dew®, and 3 bottles of IBC®. (a) What is the probability that a bottle chosen at random is Coke? (b) What is the probability that a bottle chosen at random is either Pepsi or IBC? 14. A study on the age distribution of students at a community college yielded the following data: Age 17 and under 18–20 21–24 25–34 35–64 65 and over Probability 0.03 ??? 0.23 0.29 0.25 0.01 What is the probability a randomly selected student at the college is between 18 and 20 years old? 15. In a certain lottery, there are ten balls numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Of these, five are drawn in order. If you pick five numbers that match those drawn in the correct order, you win $1,000,000. What is the probability of winning such a lottery? 16. If you roll a die five times, what is the probability that you obtain exactly 2 fours? 1. Solve: − = − x x 3 2 1 2 2. Graph ( ) = + − f x x x4 5 2 by determining whether the graph is concave up or concave down and by finding the vertex, axis of symmetry, and intercepts. 3. Graph ( ) ( ) = + − f x x 2 1 4 2 using transformations. 4. Solve: x 4 0.01 − ≤ 5. Find the complex zeros of ( ) = − − − − f x x x x x 5 9 7 31 6 4 3 2 6. Graph ( ) = + − g x 3 5 x 1 using transformations. Find the domain, the range, and the horizontal asymptote of g. 7. What is the exact value of log 9? 3 8. Solve: ( ) − + = x x log 3 2 log 4 2 2 9. Solve the system: − + = + − = − − + − =− ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 2 15 3 3 8 2 4 27 10. What is the 33rd term in the sequence 3, 1, 5, 9, ?… − What is the sum of the first 20 terms? 11. Graph: y x 3sin 2 π ( ) = + 12. Solve the following triangle and find its area. 5 a 408 9 B C Cumulative Review The Lottery and Expected Profit When all of the possible outcomes in a probability model are numeric quantities, useful statistics can be computed for such models. The expected value, or mean, of such a probability model is found by multiplying each possible numeric outcome by its corresponding probability and then adding these products. For example, Table 2 on the following page provides the probability model for rolling a fair six-sided die. The expected value, ( ) E x , is ( ) =⋅+⋅+⋅+⋅+⋅+⋅ = E x 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6 3.5 Credit: HappyAngel 888/Shutterstock When a fair die is rolled repeatedly, the average of the outcomes will approach 3.5. Mega Millions is a multistate lottery in which a player selects five different “white” numbers from 1 to 70 and one “gold” number from 1 to 25. The probability model shown in Table 3 on the next page lists the possible cash prizes and their corresponding probabilities. 1. Verify that Table 3 is a probability model. 2. To win the jackpot, a player must match all six numbers. Verify the probability given in Table 3 of winning the jackpot. Chapter Project 938 CHAPTER 13 Counting and Probability
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