Question 515540: If P(A or B) = 0.5, P(A) = 0.2 and P(B) = 0.7, determine
P(A and B).
(Points : 3)
0.10
0.35
0.40
0.90
Found 2 solutions by stanbon, drcole:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If P(A or B) = 0.5, P(A) = 0.2 and P(B) = 0.7, determine
P(A and B).
----
P(A and B) = P(A) + P(B) - P(A or B)
----
= 0.2 + 0.7 - 0.5
---
= 0.4
===========
Cheers,
Stan H.
============
(Points : 3)
0.10
0.35
0.40
0.90
Answer by drcole(72) (Show Source):
You can put this solution on YOUR website! The inclusion-exclusion principle tells us that:
P(A or B) = P(A) + P(B) - P(A and B)
We subtract P(A and B) because A and B is included in both A and B, so by just taking P(A) + P(B), you are double-counting the overlap P(A and B).
We know that P(A or B) = 0.5, P(A) = 0.2, and P(B) = 0.7. We substitute these values into the formula above and solve for P(A and B).
0.5 = 0.2 + 0.7 - P(A and B)
0.5 = 0.9 - P(A and B) (simplify)
-0.4 = -P(A and B) (subtract 0.9 from both sides)
0.4 = P(A and B) (negate both sides)
So P(A and B) = 0.4.
|
|
|
