A product engineer has developed the following equation for the cost of a system component: C = (10P)2, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of 3 identical components, all of which must operate for the system to operate. The engineer can spend $253 for the 3 components.
What is the largest component probability that can be achieved? (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
Probability