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Post by Flying Monkeys on Jan 5, 2020 12:00:21 GMT
A film and its sequel are available as follows:
- rent separately for £3.50 each - buy separately for £5 each - buy both together for £8
Each film could be good or bad - you have no prior knowledge. At the end, you must own the first film if it is good, you will only watch the 2nd if the first was good and you must own the 2nd at the end if it was also good.
So - What route should you take to minimise your cost per good film owned at the end assuming it is 50/50 probability that a film is good or bad?
For example:
- you could rent the first one (3.5) and if it's good buy them both (total spend £11.50) - they could both be good so that's 5.75 per good film - or the 2nd one could be shit so that's 11.5 on 1 good film - you could rent the 1st, if good rent 2nd, if good buy both, so total spend £15 for 2 good films, i.e. £7.5 per film - you could rent the 1st, if good rent 2nd, if shit buy the 1st only, so total spend £12 for 1 good films, i.e. £12 per film
- etc etc - so what's the minimum you can spend per good film when you apply the 50/50 probability as well?
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Post by Flying Monkeys on Jan 7, 2020 11:37:25 GMT
Here are my workings, I assume yours are similar: A lot depends on the weighting you place on how important it is to end up with good films and how much is spent. In my weighting, buying them both upfront is the best option as can be seen in the final score column. In the end, I rented one, it turned out to be okay (neither good nor bad), which I did not build into the model, so rented the second which turned out to be okay only as well. So I spent £7 and ended up with no good films. If I had spent a pound more, I could have ended up with two films that I probably wouldn't have watched again, so I think this was the best result. I am, of course, talking about the Jack Reachers.
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