At the end of a course the final grade is decided with the help of an oral examination. There are a total of 30 possible subjects each written on a piece of paper. Of them, 15 is generally considered easy. (a) Each student enrolled in the class, one after another, draws a subject from the possible 30 without revealing it. Then they get a period of 30 min to prepare their answer. Suppose, I can choose the place to draw my subject and naturally I want to draw an easy subject. I can choose to draw first or fifth. Which position should I choose to maximize my chances to draw an easy subject? (b) The professor thinks the class was particularly bad and he wants to punish the first student drawing the subjects. So he changed the rules a bit. He distributes the subjects among two urns. The students first choose an urn and then draw a subject at random from the urn chosen. How should the professor distribute the subjects to maximize the chances that the first student will get a hard subject? Note: You may use a computer to answer this question.
At the end of a course the final grade is decided with the help of an oral examination. There are a total of 30 possible subjects each written on a piece of paper. Of them, 15 is generally considered easy. (a) Each student enrolled in the class, one after another, draws a subject from the possible 30 without revealing it. Then they get a period of 30 min to prepare their answer. Suppose, I can choose the place to draw my subject and naturally I want to draw an easy subject. I can choose to draw first or fifth. Which position should I choose to maximize my chances to draw an easy subject? (b) The professor thinks the class was particularly bad and he wants to punish the first student drawing the subjects. So he changed the rules a bit. He distributes the subjects among two urns. The students first choose an urn and then draw a subject at random from the urn chosen. How should the professor distribute the subjects to maximize the chances that the first student will get a hard subject? Note: You may use a computer to answer this question.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:At the end of a course the final grade is decided with the help of an oral examination. There are a total of
30 possible subjects each written on a piece of paper. Of them, 15 is generally considered easy.
(a) Each student enrolled in the class, one after another, draws a subject from the possible 30 without
revealing it. Then they get a period of 30 min to prepare their answer. Suppose, I can choose the place to
draw my subject and naturally I want to draw an easy subject. I can choose to draw first or fifth. Which
position should I choose to maximize my chances to draw an easy subject?
(b) The professor thinks the class was particularly bad and he wants to punish the first student drawing the
subjects. So he changed the rules a bit. He distributes the subjects among two urns. The students first
choose an urn and then draw a subject at random from the urn chosen. How should the professor
distribute the subjects to maximize the chances that the first student will get a hard subject? Note: You
may use a computer to answer this question.
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