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September 21st, 2018, 04:36 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 200 Thanks: 2  Probability Questions
Let A be the sample space with six elements A = { a, b, c, d, e, f }. Let P be the probability distribution P(a) = 0.05 P(b) = 0.1 P(c) = 0.05 P(d) = 0.1 P(e) = 0.3 P(f) = 0.4 Consider the events X = {a, b, c}, Y = {b, d, e}, Z = {b, e, f} Evaluate the following: Are the following answers correct?? 1. P(X) = 0.05 + 0.1 + 0.05 = 0.2 2. P(Y) = 0.1 + 0.1 + 0.3 = 0.5 3. P(Z) = 0.1 + 0.3 + 0.4 = 0.8 4. P(X,Y) = P(X and Y) = P({b}) = 0.1 5. P(XY) = P(X and Y) / P(Y) = 0.1 / 0.5 = 0.2 
September 21st, 2018, 06:34 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,201 Thanks: 1156 
[QUOTE=zollen;599403] Are the following answers correct?? yes 
September 22nd, 2018, 07:56 AM  #3 
Senior Member Joined: Jan 2017 From: Toronto Posts: 200 Thanks: 2 
6. P(YX,Z) = P(X,ZY)*P(Y)/P(X,Z) = P(XY) * P(ZY) * P(Y) / P(X,Z) Since P(XY) = 0.2 P(ZY) = P(Z and Y) / P(Y) = 0.8 P(Y) = 0.5 P(X,Z) = P(X and Z) = P({b}) = 0.1 Therefore P(YX,Z) = 0.2 * 0.8 * 0.5 / 0.1 = 0.8 Am I correct? 

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