Solve by creating a decision tree with a payout table.

Weve been looking into options for strengthening our security system, but we can seem to reach a consensus as to how to go about it. Could you provide us with a good map for looking at how to wade through all the possibilities and get at the most cost-effective solution? Heres what we can tell you:

The first option is to leave the security system as is. If we do, theres about a 5% chance of somebody managing to break in. Should they manage to do that, theres a roughly 10% chance they could get away with some very valuable equipment. This could cost us as much as $5,000,000. At that point, we could eat the loss or attempt to get the equipment replaced through our insurance company. Some of our more experienced employees have seen that this is not guaranteed to work out since insurance companies usually try to find a way to avoid paying out. We anticipate a 60% chance of a full payout, in which case we break even. Theres also a 35% that they only give us a partial payout, in which we expect to only make back up to $3,000,000. They also might reject the claim outright and pay us nothing.

Some of the team are saying that we need to update our system, but only a simple upgrade. This simple upgrade would cost us $1,000,000 and lower the probability of a break-in to 3%. From there, everything else stays the same.

A smaller constituent of our group is pulling for a more intense system update costing $10,000,000. The benefits of this are that it would decrease the probability of a break-in even further, and our insurance company would be more likely to payout. The probability of a break-in would drop to 1%, the probability that anybody who breaks in could steal our equipment drops to 5%, and the insurance would be 80% likely to give us a full payout and 15% likely to give us a partial payout.

Another group is saying that all we really need to do is pay for better insurance, ($5,250,000) given that the chance of a break-in is already so small. This wouldnt decrease the chances of a break-in, but it does increase the chances of getting a full payout to 75% and a partial payout to 22%.

We would like to know the best course of action and what we should expect the costs to be for each possibility.