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.
If they were to connect an identical, backup gyroscope with a .90 reliable switch to the primary gyroscope, what would be the reliability of the gyroscope function during a launch?
0.889
0.91
0.504
0.3
0.7