ADM2303 Assignment two Probability Theory | Complete Solution

ADM2303 -Summer 2015
Assignment two
Probability Theory

Part I of the assignment :
Must be done via MySytatlab

Part II of the assignment :

Please don't forget to complete your signed statement of Academic Integrity within the body of your solution Submit a PDF of your type-written (i.e., not handwritten) solution (recall that a submission cannot be marked unless it is in PDF format). Submit your assignment via blackboard learn by due-date Monday, June 15, 11:59 P.M. For this assignment you don't require to use MiniTab, Excel or any statistical tool Make sure to provide detailed calculations and steps of how you arrived at your answer whenever needed.

Question 1.
Canada conducts a census every ve years. Federal, provincial, and local governments use census data to shape public policy. In 2006, Canada tried something no other country had ever tried - census questionnaires that could be completed online. Sixty-six percent of households completed their census questionnaire by the May 16 deadline. (Households that did not respond by the deadline received follow-up letters and phone calls.) Nineteen percent of households responded online ; sixteen percent of households responded on time and online

a) What percent of households led on time or led online ?
b) What percent of households did not le on time but used the online service when they eventually responded ?
c) What percent of households led on time but did not le online ?
d) What percent of households neither led on time nor online ?


Question 2.
Part one - Seventy-six percent of Ottawans speak English only when they're at home, 10% speak only French, 11% speak a non-ocial language, and the remainder speak more than one language. You are conducting a poll by calling Ottawans at random. In your rst three calls, what is the probability you talk to :

a) Only people who speak only English at home ?
b) No people who speak only French at home ?
c) At least one person who speaks a non-ocial language at home ?

Part two - Sixty percent of Ottawans drive their own vehicles to work, 7% ride as passengers in someone else's vehicle, 22% take public transit, 10% walk or cycle, and the remainder get to work some other way. Again you are conducting poll by calling Ottawans at random. In your rst four calls, what is the probability you talk to :

a) Only people who drive their own vehicles to work ?
b) No one who takes public transit to work ?
c) At least one person who walks or cycles to work ?

Question 3.
A survey of students in a large Statistics for Management class asked about their birth order (1 = oldest or only child ) and which faculty of the university they were studying under. Here are the data :
Birth order Faculty 1 or only 2 or more Total
Art & Sciences 34 23 57
Agriculture 52 41 93
Human Ecology 15 28 43
Other 12 18 30
Total 113 110 223
a) If we select a student at random, what is the probability that the person is an Art & Sciences student who is a second child (or more)?
b) Among the Art & Sciences students, what is the probability that a student is a second child (or more) ?
c) Among second children (or more), what is the probability that the student is enrolled in Art & Sciences ?
d) What is the probability that a rst or only child is enrolled in the Agricultural College ?
e) What is the probability that an Agriculture student is a rst or only child ?
f) Are enrolling in Agriculture and Human Ecology disjoint ? Explain.
g) Are enrolling in Agriculture and Human Ecology independent ? Explain.
h) Are being rst-born and enrolling in Human Ecology disjoint ? Explain.
i) Are being rst-born and enrolling in Human Ecology independent ? Explain.

Question 4.
Elizabeth if ying from Moncton to Vancouver with a connection in Montreal. The probability that her rstight leaves on time is 0.15. If the ight is on time, the probability that her luggage will make the connecting ight in Montreal is 0.95, but if the rstight is delayed, the probability that the luggage will make it is only 0.65.
a) Draw a "tree diagram" and organize all the information in the diagram.
b) Are the rstight and leaving on time and the luggage making the connection independent events? Explain.
c) What is the probability that Elizabeth's luggage arrives in Vancouver with her ?
d) Suppose that her dad picks her up at the Vancouver airport and her luggage is not there. What is the probability that Elizabeth's rstight was delayed ?