Problem 1 Suppose you have a bag filled with 60 marbles of the same size. 14 of the marbles are catseyes, 8 are alleys, 10 are tri-lites, 12 are aggies, and 16 are clearies. Suppose you draw two marbles from the bag in quick succession, noting the marble type for each draw. Consider the following events: Y, = {"1st marble is a clearie"} • X1 = {"1st marble is not a clearie"} Y2 = {"2nd marble is a clearie"} • X2 = {"2nd marble is not a clearie"} Do the following: a) Find P(Y2|Y1), P(X2|X1), P(Y2|X1), and P(X2|Y1) b) Find P(Y1), P(X1), P(Y2), and P(X2) c) Find P(Y1|Y2), P(X1\X2), P(X1|Y2), and P(Y1|X2) d) Determine if the following pairs of events are independent: Y, & Y2, Y1 & X2, X1 & Y2, X1 & X2 e) How would returning the first drawn marble to the bag before drawing the second marble affect the independence of the above pairs of events (if at all)?
Problem 1 Suppose you have a bag filled with 60 marbles of the same size. 14 of the marbles are catseyes, 8 are alleys, 10 are tri-lites, 12 are aggies, and 16 are clearies. Suppose you draw two marbles from the bag in quick succession, noting the marble type for each draw. Consider the following events: Y, = {"1st marble is a clearie"} • X1 = {"1st marble is not a clearie"} Y2 = {"2nd marble is a clearie"} • X2 = {"2nd marble is not a clearie"} Do the following: a) Find P(Y2|Y1), P(X2|X1), P(Y2|X1), and P(X2|Y1) b) Find P(Y1), P(X1), P(Y2), and P(X2) c) Find P(Y1|Y2), P(X1\X2), P(X1|Y2), and P(Y1|X2) d) Determine if the following pairs of events are independent: Y, & Y2, Y1 & X2, X1 & Y2, X1 & X2 e) How would returning the first drawn marble to the bag before drawing the second marble affect the independence of the above pairs of events (if at all)?
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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Parts d & e
Transcribed Image Text:Problem 1
Suppose you have a bag filled with 60 marbles of the same size. 14 of the marbles are catseyes, 8 are
alleys, 10 are tri-lites, 12 are aggies, and 16 are clearies. Suppose you draw two marbles from the bag
in quick succession, noting the marble type for each draw. Consider the following events:
Y, = {"1st marble is a clearie"}
• X1 = {"1st marble is not a clearie"}
Y2 = {"2nd marble is a clearie"}
• X2 = {"2nd marble is not a clearie"}
Do the following:
a) Find P(Y2|Y1), P(X2|X1), P(Y2|X1), and P(X2|Y1)
b) Find P(Y1), P(X1), P(Y2), and P(X2)
c) Find P(Y1|Y2), P(X1\X2), P(X1|Y2), and P(Y1|X2)
d) Determine if the following pairs of events are independent: Y, & Y2, Y1 & X2, X1 & Y2, X1 & X2
e) How would returning the first drawn marble to the bag before drawing the second marble affect the
independence of the above pairs of events (if at all)?
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