STAT1181 - Probability - Statistics Assignment Help

Assignment Task

Q1. From a recent study, 80% of first-year university students have taken introductory French and 60% of them have taken Calculus I. The study also showed that 50% them have done both.
Define event A as First-year university students having taken introductory French. Define event B as First-year university students having taken Calculus I.
a) When a first-year university student is randomly selected, what is the probability that one has taken either introductory French or Calculus I?
b) When a first-year university student who has taken introductory French is randomly selected, what is the probability that one has also taken Calculus I?
c) Are events A and B independent to each other?

Q2. Suppose students are not allowed to take both introductory French and introductory Spanish for credits – therefore no one would take both. From a recent study, 60% of first-year university students have taken introductory French and 20% of them have taken introductory Spanish. Define event A as: first-year university students having taken introductory French. Define event B as: first-year university students having taken introductory Spanish.
a) When a first-year university student is randomly selected, what is the probability that one has taken either introductory French or introductory Spanish?

Q3. It is estimated that 30% of university students are taking five or more classes this semester (let us call them full-load students). Among the full-load students, 20% are working part-time. On the other hand, among the non-full-load students, 60% are working part-time. Define event A as: university students taking five or more classes (or being full-load students).
Define event B as: university students working part-time.
a) When a university student is randomly selected, what is the probability that one is a full-load student and working part-time?
b) When a university student is randomly selected, what is the probability that one is working part-time but not taking full-load?
c) Consider Exercise 2, there are two stages because there are two events. And because event A is given (or its complement), it goes to the first stage naturally. Then, event B goes to the second stage. Draw a tree diagram to show the situation from Exercise 2.
d) When a student is randomly selected from the group of students who are working part-time, what is the probability that one is a full-load student?
e) When a student is randomly selected from the group of students who are not working parttime, what is the probability that one is not a full-load student?

Q4. Suppose we are to select one student at random from a pool of 408 students, categorized based on their majors and whether they are studying full time or part time, as shown in the accompanying table.
Art & Science Business Other Total
Full Time 84 112 42 238
Part Time 60 80 30 170
Total 144 192 72 408
A student is randomly selected. Define event A as selecting a Business student, event B as electing a full-time student. Are the two events independent?

Q5. The educational level and employment status for a number of adults in a city is summarized on the accompanying table. One person is to be selected at random.
No Hight School
High School
Some Post-secondary Education
Post-secondary Degree
Total
Employed 20 85 65 110 280
Unemployed 18 31 17 9 75
Total 38 116 82 119 355
a) What is the probability the selected person has a post-secondary degree or is employed?
b) Are the events “selecting a person with a post-secondary degree” and “selecting an employed person” disjoint (mutually exclusive)?
c) What is the probability of selecting a person with no high school education?

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