SOLUTION: what is the probability of (AnB) if P(A) =.50; P(B) =.20; P(A/B) =.75 P(B/A) =.30 P(AuB) =.55

Question 367174: what is the probability of (AnB) if P(A) =.50; P(B) =.20; P(A/B) =.75 P(B/A) =.30 P(AuB) =.55
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
what is the probability of (AnB) if P(A) =.50; P(B) =.20; P(A|B) =.75
P(B|A) =.30 P(AuB) =.55

This gives more information that you need.  So you can do the problem by any of
three methods using different ones of those pieces of information.  Here are all
three methods:

Method 1:

          P(AnB)  
P(A|B) = --------
           P(B)

          P(AnB)  
  .75 = --------
           .20

Multiply both sides by .20


(.20)(.75) = P(AnB)

       .15 = P(AnB)

You only needed P(A|B) and P(B), You did not need either of the other two.

------------------------------
Method 2:

          P(BnA)  
P(B|A) = --------, ans since BuA and AuB are the same,
           P(A)

          P(AnB)  
P(B|A) = --------
           P(A)

          P(AnB)  
  .30 = --------
           .50

Multiply both sides by .50


(.50)(.30) = P(AnB)

       .15 = P(AnB)

You only needed P(B|A) and P(A), You did not need either of the other two.

------------------------------

Method 3:

P(AuB) = P(A) + P(B) - P(AnB)

  .55  = .50  + .20  - P(AnB)

  .55  = .70  - P(AnB)

P(AnB) = .15

For this method you only needed P(A), P(B), and P(AuB). You did not need
either of the other two.

Edwin

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