If we undertake a campaign to contact our 30 day overdue group of customers, what is our overall probability of success given the following probabilities:
50% chance of having their e-mail on file
20% chance of a customer paying their bill without us contacting them
30% chance of a customer reading the e-mail we send them
30% chance of a customer making a payment if they read the e-mail
etc.

Question

If we undertake a campaign to contact our 30 day overdue group of customers, what is our overall probability of success given the following probabilities:
50% chance of having their e-mail on file
20% chance of a customer paying their bill without us contacting them
30% chance of a customer reading the e-mail we send them
30% chance of a customer making a payment if they read the e-mail
etc.

Anonymous · Accepted Answer

Use a decision tree.

Anonymous · Answer

It's ~25%. .5 x .3 x .3 = .045 or 4.5% success rate from emailing. Add to that the unprompted payment rate (.2 or 20%) and get 24.5%

Anonymous · Answer

^That method won't work because it's possible that there are those on the email list that would respond without an email, so there would be some overlap, which means you can't just add the two together. Easiest way to approach it would be to draw some sort of Venn Diagram

Anonymous · Answer

this is likely an applied probability question: My answer is to apply total probability formula here.

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