2018 Jan

Question 3

(b)

An unmanned monitoring system uses high-tech video equipment and

microprocessors to detect intruders. A prototype system has been developed and

is in use outdoors at a weapons munitions plant. The system is designed to

detect intruders with a probability of 0.90. However, the design engineers

expect this probability to vary with weather condition. The system

automatically records the weather condition each time an intruder is detected.

Based on a series of controlled tests, in which an intruder was released at the

plant under various weather conditions, the following information is available:

Given the intruder was, in fact, detected by the system, the weather was clear

75% of the time, cloudy 20 % of the time, and raining 5% of the time. When

the system failed to detect the intruder, 60 % of the days were clear, 30%

cloudy, and 10% rainy. Compute the probability of detecting an intruder, given

rainy weather conditions. (Assume that an intruder has been released at the

plant).