An experimental deepsea living sphere has been designed with

An experimental deep-sea living sphere has been designed with two independent systems for detecting excessive water pressure. ONe warning system has a probability of .99 of operating correctly and the other has a probability of .98 of operating correctly. What is the probability that either one or the other warning system will operate correctly?

Solution

probability of operating correctly for the first warning system = 0.99

probability of operating incorrectly for the first warning system = 1 - 0.99 = 0.01

probability of operating correctly for the second warning system = 0.98

probability of operating incorrectly for the second warning system = 1 - 0.98 = 0.02

probability that either one or the other warning system will operate correctly is given by

probability that first warning system operates correctly * probability that the second warning system does not operate correctly + probability that second warning system operates correctly * probability that the first warning system does not operate correctly

probability that either one or the other warning system will operate correctly = 0.99 * 0.02 + 0.98 * 0.01

                = 0.0296