I'm curious about how a decision tree of this scenario would be.
I sketched one on my agenda book, which I reproduce below.
But I could not fit Earthquake on it, because it is simultaneous with Burglary when it happens, and in the decision tree there is no space for simultaneous events.
How...
You are right. The scenario already states that B happened, so it should be 1 (100%) instead of just 0.001.
Fixing:
0.00171;
0.844308;
0.000005;
0.002994.
Or could also be represented as:
0.171%;
84.4308%;
0.0005%;
0.2994%.
But I still don't see how these numbers can help me "work out ##...
Hey, a Truth Table I know how to make!
I learned it from classes about binary calculation and also philosophy classes.
Here it is:
#
Burglary
JohnCalls
Alarm
Earthquake
1
T
T
T
T
2
T
T
T
F
3
T
T
F
T
4
T
T
F
F
Entering the numbers on it, it becomes:
#
Burglary...
So, I must use just Bayes Theorem instead of the formula that Mark44 shown?
On my first post, I pointed out that my doubt is how to discover ## P(B | J) ## and ## P(J) ## , in order to complete the Bayes Theorem . Am I focusing wrongly?
Fine, applying it to the problem:
$$P(J | B) = \frac{P(J \cap B)}{P(B)}$$
P(R) is 0.001, great!;
P(J ∩ R) I don't know how to deduce. Could you give me a hint?
I mean, there is no direct relationship between J and R, because there is A (Alarm) in the middle of the path.
Sorry for not being clear enough. Here is the description of the book in my own words:
There is a house, and this house has an Alarm;
The Alarm detects Burglary, but also sometimes respond to minor Earthquakes;
John and Mary are neighbours of said house and will call you, the resident, if they...
Questions:
P (JohnCalls|Burglary) ?
Why?
Source of the image: Artificial Intelligence: A Modern Approach - Third Edition, by Stuart Russell and Peter Norvig.
My attempt at solving: using Bayes' Theorem = P (A|B) = ( P(B|A) * P(A) ) / P(B)
P(JohnCalls|Burglary) = P(J|B) = ( P(B|J) * P(J) /...