SOLUTION: The following probabilities are given for two events A and B: P(A)=1/4, P(B)=1/3, P(A|B)=1/2. Find P(A or B). Could you show me how you arrived at solution so I can understan

Algebra ->  Probability-and-statistics -> SOLUTION: The following probabilities are given for two events A and B: P(A)=1/4, P(B)=1/3, P(A|B)=1/2. Find P(A or B). Could you show me how you arrived at solution so I can understan      Log On


   

Question 214730: The following probabilities are given for two events A and B: P(A)=1/4, P(B)=1/3, P(A|B)=1/2. Find P(A or B).

Could you show me how you arrived at solution so I can understand the process. Thank you for helping.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The following probabilities are given for two events A and B: P(A)=1/4, P(B)=1/3, P(A|B)=1/2. Find P(A or B).
-------------------------
Law: P(A or B) = P(A) + P(B) - P(A and B)
---
Your Problem:
P(A or B) = (1/4) + (1/3) - P(A and B)
--
But P(A and B) = P(A|B)*P(B)
So P(A and B) = (1/2)(1/3) = 1/6
--------------------------------------
Therefore P(A or B) = (1/4) + (1/3) - 1/6
---
lcd = 12
---
P(A or B) = [3 + 4 - 2]/12 = 5/12
=============================================
Cheers,
Stan H.