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September 21st, 2018, 03:36 PM   #1
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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
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September 21st, 2018, 05:34 PM   #2
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[QUOTE=zollen;599403]
Are the following answers correct??

yes
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September 22nd, 2018, 06:56 AM   #3
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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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