College Okanagan Math 111 (71) Fall 2007 Assignment Three
Instructor: Clint Lee Due: Tuesday December 11 Instructions. Do all parts of all 8 questions. Show all significant steps in your work. You will not receive any marks for just an answer, even if it is correct. Use complete English language sentences to answer questions where a written answer or explanation is required. The number of points for each question is given in the left margin, total 60. The questions in this assignment consist of all of the questions on Term Test Two plus additional questions. The questions that appeared on Term Test Three are labelled with a number in square brackets, giving the corresponding number of the question on the test. 1. [2] [2] [3] You are to create a secret four-digit code for your ATM card using the digits 0 to 9. (a) [1a] How many different codes can be made if digits can repeat? (b) [1b] If you are only allowed to use a digit once, how many different codes can be made? (c) If the product of the digits in the number must be even, how many different codes can be made?
2. [1] [2] [3]
A college student plans to select courses from among four possible foreign language courses, seven possible mathematics courses, and five possible economics courses. (a) In how many ways can the student select three courses, one of each type? (b) In how many ways can the student select five courses made up of two of the foreign language courses, two of the economics courses and one of the mathematics courses? (c) In how many ways can the student select six courses made up of two or three of the foreign language courses, one of the mathematics courses, and the rest from the economics courses.
3. [2] [3] [3]
There are five married couples (assume they are heterosexual) at a party. (a) [2a] How many ways are there to choose and arrange five of the people who are to be seated in a row as part of a party game? (b) [2b] For another party game six people are chosen with an equal number of men and women. How many ways are there of choosing this group of six people? (c) [2c] When all of the people at the party are seated for dinner a toast is proposed and everyone touches their glass with every other person at the table except their spouse. How many glass touches take place?
Math 111 (71) Fall 2007
Assignment Three
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[2] [3] [3]
(a) [3a] List the sample space for this experiment as a set of ordered pairs of numbers, (s, d), where s is the number on the spinner and d is the number on the die. (b) [3b] Give the probability distribution for this experiment by assigning a probability to each of the outcomes. (c) [3b] Let E be the event that the sum of the numbers on the spinner and the die is odd, and let F be the event that the number on the spinner is zero. Describe events E and F by listing the outcomes in each event, and find Pr( E) and Pr( F ). (d) For the events E and F defined in part (c) express probability below in terms of E and F and find the probability: the number on the spinner is Pr zero or the sum of the numbers on the spinner and the die is even
[3]
5. [3] [1] [2]
Let A, B, and C be three events for which Pr( A) = 0.4, Pr( B) = 0.6, and Pr(C ) = 0.5. Further, events A and B are independent, event B and C are independent, and events A and C are mutually exclusive. (a) [4a] Determine the values of Pr ( A B), Pr ( B C ), and Pr ( A C ). (b) [4b] Explain why must it be true that Pr ( A B C ) = 0. (c) [4c] Determine the values of Pr ( A B C ) and Pr ( A B C ). You may find it helpful to use the three circle Venn diagram shown.
A B
C
6. [2] [3] [1]
A lot of 20 Pentium V processors contains 4 defective processors. A sample of 4 processors is chosen at random and without replacement from the lot. Find the probability that: (a) [5a] All of the processors in the sample are non-defective. (b) [5b] At least 3 of the processors in the sample are non-defective. (c) [5c] At least one of the processors is defective.
An experiment consists of spinning the spinner shown, in which getting a two is twice as likely as getting a zero or a one, and then rolling a single six-sided die with a one on three faces, a two on two faces, and a three on one face, so that it is three times as likely to get a one as it is to get a three and twice as likely to get a two as it is to get a three.
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Math 111 (71) Fall 2007
Assignment Three
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A sample of dog owners shows that 25% of dog owners with one dog have visited a veterinarian in the last year, 40% of dog owners with two dogs have visited a veterinarian in the last year, and 60% of dog owners with more than two dogs have visited a veterinarian in the last year. Further, it is known that 70% of dog owners own just one dog, 20% own two dogs, and 10% own more than two dogs. (a) [6a] Define appropriate events for this problem and fill in whichever of the tree diagrams below which is appropriate for this problem. Put all probability values that you are given or can calculate on the diagram.
[4]
[2] [2]
(b) [6b] A dog owner is selected at random. Find the probability that the person selected has visited a veterinarian in the last year. (c) [6c] A dog owner is selected at random. If the person selected has visited a veterinarian in the last year, find the probability that the person owns no more than two dogs.
8.
A survey of 500 employees in the IT industry is conducted to determine the relation between the marital statu...