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Math 112A Probability Rewrite Assignment - 2009 MacMillan/ Manuel /31 Name:_______________ Part I. Multiple Choice. Choose the best answer and place it in the corresponding blank at the end. (value 15) 1. Suppose you do not replace the 1st card before selecting a 2nd from a well-shuffled deck. Which is used to find the probability that the outcome will be two black face cards? a) 12 11 b) 6 5 c) 6 6 d) 6 6 52 51 52 51 52 52 52 52 2. The value 5! is equivalent to: a) 5P1 b) 5P5 c) 5C5 d) 5C1 3. Which can be used to find how many different license plate numbers are possible in the form "letter, number, letter, number, letter, number" if the first letter cannot be an A, the number 0 is not possible and no letter or number can be repeated? a) 25x9x24x8x23x7 b) 25x9x25x8x24x7 c) 25x10x25x9x24x8 d) 24x9x24x8x23x7 4. A multiple choice test has 12 questions with each question providing four choices for answers (A, B, C or D). How many different sets of answers are possible for the test? a) 16777216 b) 20736 c) 48 d) 479001600 5. What is the probability of selecting a ten or a red card from a well-shuffled deck of cards? a) 15 b) 7 c) 15 d) 29 26 13 52 52 6. What is the probability of selecting an Ace or a red Queen from a well-shuffled deck of cards? a) 3 b) 5 c) 3 d) 2 26 52 52 13 7. A red die and a blue die are tossed. What is the probability that the red die shows a three and the blue die shows a number greater than three? a) 1 36 b) 1 c) 1 d) 2 18 12 3 8. Which expression can be used to determine the number of permutations when arranging all the letters in the word “LETTERS”? a) 7! b) 7! c) 7! d) 7! 2! 4! 2!2! 9. A committee of three is randomly selected from a group of 4 males and 5 females. Which can be used to determine the probability that all males will be chosen? 3 4 C3 4 C3 1 a) b) c) d) C C C 4 3 9 3 9 3 9 C4 10. A bag contains 10 green and 4 blue marbles. Suppose you removed 2 marbles at random, without replacement. What is the probability that the two marbles will be blue? a) 4 b) 6 c) 7 d) 6 49 91 27 7 11. Which of the following represents the probability of Dan, Erin, and Jane placing first, second, and third (in that order) out of a group of 8 runners? 1 1 1 a) 1 b) c) d) 8! 8 P5 8 C3 8 P3 12. There are 6 boys and 5 girls on a committee. Four members of the committee will be randomly selected to go to a conference. Which of the following represents the probability that only 1 girl is selected to go to the conference? a) 5C3 x 6C1 b) 6C3 x 5C1 c) 6C3 + 5C1 d) 6C3 x 5C1 11C4 11C3 11C4 11C4 13. Which of the following lists is the first 4 elements of the 16th row of Pascal’s Triangle? a) 1 16 120 560 b) 1 16 120 240 c) 1 16 240 3360 d) 1 16 256 4096 14. Which of the following is equivalent to the first 4 terms of (x + 1)12 ? a) x12 + 11x10 + 66x9 + 495x8 c) x12 + 12x11 + 66x10 + 220x9 12 11 10 9 b) x + 12x + 220x + 495x d) x11 + 11x10 + 66x9 + 220x8 15. Which of the following is equivalent to x6 + 6x5y +15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6 ? a) (x + 1)6 b) (x + y)5 c) (x + y)6 d) (x + 1)y Answers: 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. ______ 7. ______ 8.______ 9.______ 10. ______11. _____ 12._____ 13._____ 14. ______ 15. ______ Part II. Open Response. Show work in the space provided to receive full value. (Value 16) 1. Complete the following Venn Diagram for a deck of cards. Face Cards spades _____ _______ 2. Write the first four terms of the expanded form of (x + y) 16. _____ ____ _____ (value 2) (value 2) _____ 3. Jessie and Paige are soccer players taking penalty kicks in a shootout. Jessie typically averages three out of every five shots while Paige averages one out of every four. Construct an area model diagram for this situation and use it to determine the probability that Jessie or Paige make their shots. (value 3) Area Model Diagram 4. What is the probability of selecting a Ten or a club from a standard deck of 52 cards? (value 3) 5. Consider the Scratch-and-Win ticket to the left: IPod DVD DVD DVD IPod DVD Try Again IPod DVD you can scratch only three boxes you must scratch three identical boxes to win a prize two possible prizes to be won – an IPod or a DVD Determine the probability of winning on this ticket. (value 3) 6. A committee of 6 people is selected from a group of 8 females and 7 females. What is the probability that there are exactly four males selected for the committee? (value 3)