interpret conditional probabilities and inferring ratios


New Member
Hi All

First time here and its been a long time since I studied probability...was hoping someone could assist in the interpretation of some data I have gathered.

From some customer and historical contact data I am trying to tell a story along the lines of 'customers who are contacted are X more likely to stay with our business'.

I have created a tree diagram that has the following (modified) results:

1: P(Contacted)=0.20
2: P(~Contacted)=0.80

3: P(Stay/Contacted)=0.9
4: P(~Stay/Contacted)=0.1
5: P(Stay/~Contacted)=0.6
6: P(~Stay/~Contacted)=0.4

I am trying to develop a ratio that can tell a simple story to others in my organisation (if there is one!). For example, I was going to suggest the 3-6 above shows the following:

If you are contacted you are 9 times more likely to stay than go (0.9/.01);
while you are only 1.5 times more likely to stay than go if you are not contacted (0.6/0.4).
Therefore people are 4 times more likely to stay if they are contacted (9/1.5).

Is what I have done above completely wrong? If so is there a way I can achieve a similar interpretation?

Many thanks for any and all commentary & if my old stats lecturer is on this...sorry. :eek: