SOLUTION: The Technically Techno company has several patents for a variety of different flash memory devices that are used in computers, cell phones, and a variety of other things. A compet

Question 1194655: The Technically Techno company has several patents for a variety of different flash memory devices that are used in computers, cell phones, and a variety of other things. A competitor has recently introduced a product based on technology very similar to something patented by Technically Techno last year. Consequently, Technically Techno has sued the other company for patent infringement. Based on the facts in the case as well as the record of the lawyers involved, Technically Techno believes there is a 40% chance that it will be awarded $300,000 if the lawsuit goes to court. There is a 30% chance that Technically Techno will be awarded only $50,000 if it goes to court and wins, and there is a 30% chance that Technically Techno will lose the case and be awarded nothing. The estimated cost of legal fees if Technically Techno goes to court is $50,000. However, the other company has offered to pay Technically Techno $75,000 to settle the dispute without going to court. The estimated legal cost of this would be only $10,000. If Technically Techno wished to maximize the expected gain, should it accept the settlement offer?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll refer "Technically Techno" as "Company T".

This company has patents on various devices, and it claims some other competitor is stealing company T's ideas.

If Company T takes the other company to court, then we have these scenarios:

Payout of...	Probability
$300,000 - $50,000 = $250,000	40% = 0.40
$50,000 - $50,000 = $0	30% = 0.30
$0 - $50,000 = -50,000 dollars	30% = 0.30

For each payout, we subtract off the legal costs ($50,000) of going to court.
The negative payout means the company lost that amount of money.

All of the probabilities mentioned add to the decimal value 1, representing 100% of the possible outcomes.
Keep in mind that I'm not talking about settlement. Right now I'm talking about lawsuit only.

Multiply each payout amount with their respective probability

Net Payout	Probability	payout*probability
$250,000	0.40	250,000*0.40 = $100,000
$0	0.30	0*0.30 = $0
-50,000 dollars	0.30	-50,000*0.30 = -15,000

Add up every result in that third column
100,000+0+(-15,000) = $85,000
This is the expected value

The company T expects, on average, the lawsuit payouts will bring in net winnings of $85,000

On the other hand, if company T settles, then they will net $75,000 - $10,000 = $65,000.

Summary:
Expected net winnings from the lawsuits = $85,000
Net amount from the settlement = $65,000

The lawsuits value is larger, so it is advantageous for the company to not settle.

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