The Pioneer Software Company has developed software for organizing and playing music on a computer. The software contains a number of unique features that have been patented so the company$$s future has looked bright.

However, it appears that a number of the patented features were copied in similar software developed by the Raider Digital Company, a huge software company with annual sales revenue in excess of $$1$ billion. The executives of Pioneer Software are distressed that Raider Digital has stolen their ideas; they fear that Raider$$s marketing power is likely to enable it to capture the market and drive Pioneer out of business.

In response, Pioneer has filed a lawsuit against Raider for patent infringement. With attorney fees and other expenses, the cost of going to trial $($win or lose$)$ is expected to be $$1$ million. Pioneer feels that it has a $60\%$ chance of winning the case, in which case it would receive $$5$ million in damages. If Pioneer loses the case, it gets nothing. Moreover, if Pioneer loses the case, there is a $50\%$ chance that the judge would also order Pioneer to pay for court expenses and lawyer fees for Raider $($an additional $$1$ million cost$).$

Raider has countered by offering Pioneer $$1\mathrm{.}5$ million to settle this case out of court.

Using decision tree analysis, determine in the steps below what Pioneer Software Company should do$.$