You are experimenting with a process for producing high-energy-density batteries. You have a contract with the government to deliver a batch of 20 batteries, due today. If you deliver them on time and they are all functional, you will get $100 000. Each battery has a 1% chance of being defective, and if any of them are defective, the government will not pay you the $100 000, but will fine you $10 000. What is the expected value to you of your contract with the government?
A)-$1 821
B)$79 970
C)$81 791
D)$82 645
E)$86 777

Question

Quizplus · Accepted Answer

The expected value is calculated by considering the probability of all batteries being functional and the probability of at least one being defective. The probability that a single battery is not defective is 0.99, so the probability that all 20 are not defective is 0.99^20. The expected value is then (0.99^20 * $100,000) + (1 - 0.99^20) * (-$10,000). This calculation results in an expected value of approximately $79,970.

You Are Experimenting with a Process for Producing High-Energy-Density Batteries