Fuzzy probability/intuition problem

jammieg

A garaged door installer installs a door for Mrs. Banks one day and after completing the job she checks it out to find that it looks great except for a small dent on the metal panelling on the outside of the building, approximately 10 cm away from the garage door, she insists that the dent was not there this morning but is not certain. The door installer claim that he doesn't recall that happening and if it did he wasn't aware of it. She says she will ask her husband later if he made the dent or remebers it before the installer came.
Setting aside the motto the customer is always right here are some arbitrary facts:
The installer makes 1 mistake every 5 doors installed and of those 1 out of 10 he is unaware of the mistake.
Mrs. Banks is not sure of herself lets say she is 80% sure the installer did it and 20% it was caused by someone or something else.
Before Mr. Banks is consulted there is a 1 in 3 chance of he also being 80% sure the installer did it, but a 2 in 3 chance of being 80% sure he did not do it.
If the combined total sureness of the two are 80% or greater on some particular outcome they will believe the installer did it.

What are the overall odds that in the morning the installer will get a call from the Bankses saying they think the installer was responsible?

The answer is entirely up for debate this is an orginal problem.

jammieg

The solution I got was a 37% probability the Bankses will call.
Ok that one's way too easy, and I'm wrong anyway. What I meant was what is the probability the installer is guilty, oh well silly problem.

Last edited by a moderator:

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving