MATH 318 Chapter 2 Quiz

Name:
There are questions on both sides of this paper. Please show your work carefully and give justifications for your answers. If you get stuck on one question, leave a comment and move on to the next. If you have time left at the end of the quiz, check your work. When you have completed the quiz you may pass it in and leave the room. You may use a calculator on this quiz, but you may not use any device with wireless communication abilities.
  1. a) (10 pts) Professor Burgiel estimates that the probability that a randomly selected playing card being a face card is 16/52 = 4/13. What is the best method to use to calculate this value (e.g. classical, relative frequency or subjective)?

     

     

    b) (15 pts) Give an example of a probability calculation that uses the relative frequency method. Be sure the method used is clear from your answer.

     

     

     

     

  2. Let A be the event that a person's primary method of transportation is by car and let B be the event that a person primarily relies on public transit. Suppose P(A) = 70% and P(B) = 25%.
    a) (15 pts) Are events A and B mutually exclusive? Justify your answer.

     

     

     

    b) (10 pts) What is the probability that a person's primary method of transportation is not by car?

     

     

  3. Central Day School, a charter school dedicated to teaching first and second grade students, collected data on their students' favorite ice cream flavors; the results are presented in the crosstabulation below and to the left.
     ChocolateStrawberry 
    First Grade7026 
    Second Grade6044 
        
        
        
        
        

    a) (15 pts) Use the blank table above and to the right to create a joint probability table.
    b) (10 pts) What is the probability that a student selected at random is in first grade?

     

     

    c) (10 pts) What is the probability that a randomly selected second grade student prefers strawberry ice cream?

     

     

    d) (15 pts) Are the events "the student is in second grade" and "the student prefers chocolate ice cream" dependent or independent? Justify your answer.

     

     

     

Bonus: (5 pts) Suppose the three primary modes of transport among students at BSU are Car (60%), Train (35%) and Bicycle (5%). A (fictional) survey of students whose main mode of transport is by car reveals that 40% are seniors, 30% are juniors, 20% are sophomores and 10% are freshmen. Suppose a freshman is selected at random, and that one quarter of all students at BSU are freshmen. What is the posterior probability that that freshman's primary mode of transport is by car?