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STAT 285 - Assignment III Due Date: July 28th , 2025 Question 1 An academic department with four faculty members must select two of its members to serve on a personnel review committee. The last names of the four faculty members are Anderson, Box, Cox and Cramer. Being on the committee is time-consuming and no one wishes to volunteer, so instead they decide to do it randomly. Each member writes their names on slips of paper, they all put them in a hat and then two slips are drawn without replacement. Whoever’s names are on those two slips gets assigned the job. a) List all the possible outcomes. – 1.5 pts For the remaining parts, assume all the outcomes listed in part (a) are equally likely. b) What is the probability both Anderson and Box are selected? – ¼ pt c) What is the probability Cramer is selected? – ¼ pt d) What is the probability that at least one of the two members whose last name begins with C is selected? – ½ pt Question 2 Consider randomly selecting a student at Universal University, and let V denote the event that the selected individual has a Visa credit card and M be the analogous event for a MasterCard. Suppose that Pr(V) = 0.5, Pr(M) = 0.4 and Pr(V  M) = 0.25. a) Describe, in terms of V, M and set operations, the event that the selected student has at least one of the two types of credit cards and then calculate its probability. – ¾ pt b) Describe, in terms of V, M and set operations, the event that the selected student has neither type of credit card and then calculate its probability. – ¾ pt c) Describe, in terms of V, M and set operations, the event that the selected student has a Visa card but not a MasterCard, and then calculate its probability. – 1 pt Question 3 Suppose we are given two events, A and B, with Pr(A) = 0.6 and Pr(B) = 0.22. a) Suppose A and B are independent, find Pr(A  B). – ¾ pt b) Instead of assuming A and B are independent, assume they are mutually exclusive, find Pr(A  B). – ¾ pt c) Again, suppose A and B are mutually exclusive, find P(A|B). – ½ pt d) Can the above events, A and B, be both independent and mutually exclusive from each other? Explain why or why not. – ½ pt

Name: stat 285 assignment iii due date july 28th 2025 question 1 an academic department with four faculty members must select two of its members to serve on a personnel review committee the last n 69866
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Description: stat 285 assignment iii due date july 28th 2025 question 1 an academic department with four faculty members must select two of its members to serve on a personnel review committee the last n 69866

          STAT 285 - Assignment III
Due Date: July 28th
, 2025
Question 1
An academic department with four faculty members must select two of its members to serve on a personnel 
review committee. The last names of the four faculty members are Anderson, Box, Cox and Cramer. Being on 
the committee is time-consuming and no one wishes to volunteer, so instead they decide to do it randomly. 
Each member writes their names on slips of paper, they all put them in a hat and then two slips are drawn
without replacement. Whoever’s names are on those two slips gets assigned the job.
a) List all the possible outcomes. – 1.5 pts
For the remaining parts, assume all the outcomes listed in part (a) are equally likely. 
b) What is the probability both Anderson and Box are selected? – ¼ pt
c) What is the probability Cramer is selected? – ¼ pt
d) What is the probability that at least one of the two members whose last name begins with C is 
selected? – ½ pt
Question 2
Consider randomly selecting a student at Universal University, and let V denote the event that the selected 
individual has a Visa credit card and M be the analogous event for a MasterCard. Suppose that Pr(V) = 0.5, 
Pr(M) = 0.4 and Pr(V  M) = 0.25.
a) Describe, in terms of V, M and set operations, the event that the selected student has at least one of 
the two types of credit cards and then calculate its probability. – ¾ pt
b) Describe, in terms of V, M and set operations, the event that the selected student has neither type of 
credit card and then calculate its probability. – ¾ pt
c) Describe, in terms of V, M and set operations, the event that the selected student has a Visa card but 
not a MasterCard, and then calculate its probability. – 1 pt
Question 3
Suppose we are given two events, A and B, with Pr(A) = 0.6 and Pr(B) = 0.22.
a) Suppose A and B are independent, find Pr(A  B). – ¾ pt
b) Instead of assuming A and B are independent, assume they are mutually exclusive, 
find Pr(A  B). – ¾ pt
c) Again, suppose A and B are mutually exclusive, find P(A|B). – ½ pt
d) Can the above events, A and B, be both independent and mutually exclusive from each other? 
Explain why or why not. – ½ pt

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