SOLUTION: 5. For two events A and B, the following probabilities are given. P(A) = 0.4, P(B) = 0.25, P(A | B) = 0.6 Use the appropriate laws of probability to calculate P(A ∪ B) .

Algebra ->  Probability-and-statistics -> SOLUTION: 5. For two events A and B, the following probabilities are given. P(A) = 0.4, P(B) = 0.25, P(A | B) = 0.6 Use the appropriate laws of probability to calculate P(A ∪ B) .       Log On


   

Question 625661: 5. For two events A and B, the following probabilities are given.
P(A) = 0.4, P(B) = 0.25, P(A | B) = 0.6
Use the appropriate laws of probability to calculate P(A ∪ B) .
( ) 0.45
( ) 0.50
( ) 0.44
( ) 0.73
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for conditional probability is

         P(A ∩ B)
P(A|B) = 覧覧覧覧 
           P(B)

Substituting the given values

         P(A ∩ B)
   0.6 = 覧覧覧覧 
           0.25

Multiply both sides by 0.25
   
  0.15 = P(A ∩ B)

Now we use the formula for P(A ∪ B)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 0.4 + 0.25 - 0.15

P(A ∪ B) = 0.50

Edwin