John Campbell, an employee of Manhattan Construction Company claims to have injured his back as a result of a fall while repairing the roof at one of the Eastview apartment buildings. He filed a lawsuit against Doug Reynolds, the owner of Eastview Apartments, asking for damage of $$1,500,000.$ John claims that the roof had rotten sections and that his fall could have been prevented if Mr$.$ Reynolds had told Manhattan Construction about the problem. Mr$.$ Reynolds notified his insurance company, Allied Insurance of the lawsuit. Allied must defend Mr$.$ Reynolds, and decide what action to take regarding the lawsuit.

Some depositions and a series of discussions took place between both sides. As a result, John Campbell offered to accept a settlement of $$750,000.$ Thus one option for Allied to pay John $$750,000$ to settle the claim. Allied is also considering making John a counteroffer of $$400,000$ in the hope that he will accept a lesser amount to avoid the time and the cost of going to trial. Allied's preliminary investigation shows that John's case is strong. Allied is concerned that John may reject their counteroffer and request a jury trial. Allied's lawyers spent some time exploring John's likely reaction if they make a counteroffer of $$400,000.$

The lawyers concluded that it is adequate to consider three possible outcomes to represent John's possible reaction to a counteroffer of $$400,000.1.$ John will accept the counteroffer and the case will be closed. $2.$ John will reject the counteroffer and elect to have a jury decide the settlement amount, or $3.$ John will make a counteroffer to Allied of $$600,000.$ If John does make a counteroffer, Allied decided that they will not make additional counteroffers. They will either accept John's counteroffer of $$600,000$ or go to trial.

If the case goes to jury trial, Allied considers three outcomes possible: $1.$ The jury may reject John's claim and Allied will not be required to pay any damages; $2.$ The jury will find in favor of John and award him $$750,000$ in damages or $3.$ The jury will conclude that John has a strong case and award him the full amount of $$1,500,000.$

Key considerations as Allied develops its strategy for disposing of the case are the probabilities associated with John's response to an Allied counteroffer of $$400,000$ and the probabilities associated with the three possible trial outcomes. Allied lawyers believe the probability that John will accept the counteroffer of $$400,000$ is $0\mathrm{.}10,$ that the probability that John will reject the counteroffer of $$400,000$ is $0\mathrm{.}40,$ and the probability that John will, himself, make a counteroffer to Allied of $$600,000$ is $0\mathrm{.}50,$ If the case goes to court, they believe that the probability the jury will award John damage of $$1,500,000$ is $0\mathrm{.}30,$ the probability that the jury will award John damages of $$750,000$ is $0\mathrm{.}50,$ and the probability that the jury will award John nothing is $0\mathrm{.}20.$

Answer these questions:

$1)$ A recommendation regarding whether Allied should accept John's initial offer to settle the claim for $$750,000($show calculations and probabilities$)$

$2)$ A decision strategy that Allied should follow if they decide to make John a counteroffer of $$400,000$

$3)$ A risk profile of your recommendation strategy