The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.What is the probability that the guidance system will perform reliably during a launch?
A)0.300
B)0.504
C)0.700
D)0.889
E)0.910

Question

Quizplus · Accepted Answer

The reliability of each component is calculated by subtracting the failure rate from 1. For the gyroscope, it's 1 - 0.3 = 0.7; for the computer, 1 - 0.2 = 0.8; and for the rocket motor, 1 - 0.1 = 0.9. The overall reliability of the system is the product of these reliabilities: 0.7 * 0.8 * 0.9 = 0.504.

The Chief of the Design Team for a New Missile