A particulate monitor has the power supply consisting of two batteries in parallel. Either battery is adequate to operate monitor. But, since the failure of one battery places added strain on other, the conditional probability that second battery will fail, given the failure of the first, is greater than the probability that first will fail. On the basis of testing it is known that 7% of monitors in question will have at least on battery failed by the end of their design life, while in 1% of the monitors both batteries will fail throughout the design life.
a) Compute the battery failure probability under normal operating conditions.
b) Compute the conditional probability that the battery will fail, given that the other has failed.