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 .90. However, the design engineers expect this probability to vary with the weather. The system automatically records the weather condition each time an intruder is detected. On the basis of a series of controlled tests in which an intruder was released at the plant under various weather conditions, the following information is available: Given that 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. Use this information to find the probability of detecting an intruder, given rainy weather. (Assume that an intruder has been released at the plant.)