My Math Forum Probability Questions

 September 21st, 2018, 03:36 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 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(X|Y) = P(X and Y) / P(Y) = 0.1 / 0.5 = 0.2
 September 21st, 2018, 05:34 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1275 [QUOTE=zollen;599403] Are the following answers correct?? yes Thanks from zollen
 September 22nd, 2018, 06:56 AM #3 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 6. P(Y|X,Z) = P(X,Z|Y)*P(Y)/P(X,Z) = P(X|Y) * P(Z|Y) * P(Y) / P(X,Z) Since P(X|Y) = 0.2 P(Z|Y) = 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(Y|X,Z) = 0.2 * 0.8 * 0.5 / 0.1 = 0.8 Am I correct?

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