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 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% of the days were cloudy, and

* 10% of the days were rainy.

Define D to be the event that the intruder is detected by the system and DC is the event that the system failed to detect the intruder.

#1 Use the above given information to develop a probability table for the data information. i.e

P(D) = 0.9 P(DC) = 0.1

P(Clear/D) = 0.75 Etc.

#2 Use the table information that you created to find the probability of “Not” detecting an intruder, given Clear weather conditions. (Assume that an intruder has been released at the plant.) ie the goal is to calculate the conditional probability, P(DC/Clear).