Katie C.

asked • 03/29/15

Compute the following conditional probabilities:

A and B in a sample space S, but assume that Pr[A] = 0.4, Pr[B] = 0.35, and Pr[A∩ B] = 0.1.
 

Compute the following conditional probabilities:

(1) Pr[A | B] =

(2) Pr[B | A] =

1 Expert Answer

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Edward C. answered • 03/29/15

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Pr[A|B] = Pr[AnB] / Pr[B] = 0.1 / 0.35 = 10/35 = 2/7 ~ 0.2857
 
Pr[B|A] = Pr[BnA] / Pr[A] = 0.1 / 0.4 = 0.25  
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Katie C.

this did not answer my question
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03/30/15

Edward C.

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Sorry maybe I did not understand your question.  (1) asks for the conditional probability of A given that B has occurred.  Since B has occurred the original sample space S is restricted to B, which occurs with probability 0.35.  Within the space of B, A occurs with probability 0.1 since the probability of A and B both occurring is 0.1.  So the probability of A given B is 0.1 / 0.35 = 10 / 35 = 2/7.  (2) is solved in a similar way.  
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03/30/15

Katie C.

it was right I was just entering it into the wrong problem. Sorry, Thanks!!
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03/30/15

Katie C.

could you help me with other problems?
 
Suppose for this problem that Pr[E] = [ 5/8] and Pr[F] = [ 3/4]. Just as in the book, Pr[(E ∪F)′] = 0.
(1) What is Pr[E | F]?

(2) What is Pr[F | E]?
 
 
 
Suppose for this problem that Pr[E] = [ 1/12], Pr[F] = [ 1/6], and Pr[E ∩F′] = [ 0/1].
(1) What is Pr[E | F]?

(2) What is Pr[F | E]?
 
 
assume that Pr[E] = 0.3, Pr[F] = 0.35, and Pr[E′∩ F] = 0.15.
Compute the following conditional probabilities:

(1) Pr[E | F] =

(2) Pr[F | E] =
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03/30/15

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