Refer to the IEEE Computer Applications in Power study of an outdoor unmanned watching system designed to detect trespassers, Exercise 3.79. In snowy weather conditions, the system detected 7 out of 10 intruders; thus, the researchers estimated the system’s probability of intruder detection in snowy conditions at .70.
a. Assuming the probability of intruder detection in snowy conditions is only .50, find the probability that the unmanned system detects at least 7 of the 10 intruders.
b. Based on the result, part a, comment on the reliability of the researcher’s estimate of the system’s detection probability in snowy conditions.
c. Suppose two of the 10 intruders had criminal intentions. What is the probability that both of these intruders were detected by the system.

Data from Exercise 3.79

An article in IEEE Computer Applications in Power (April 1990) describes “an unmanned watching system to detect intruders in real time without spurious detections, both indoors and outdoors, using video cameras and microprocessors.” The system was tested outdoors under various weather conditions in Tokyo, Japan. The numbers of intruders detected and missed under each condition are provided in the table.

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Weather Condition Clear Cloudy Rainy snowy Windy Intruders detected 21 228 226 7 185 Intruders missed 6 6. 3 10 Totals 21 234 232 10 195