Suppose the probability that Sensor Type A detects a chemical agent is 0.50. The

Question

Suppose the probability that Sensor Type A detects a chemical agent is 0.50. Therefore with only one detector, the probability of being protected is 50. These sensors operate independently. You will perform the necessary actions - putting on protective gear, heading for shelter, and even leaving the area - if you hear a single alarm, no matter how many Type A detectors you have. What is the probability of protection if you have 3 Type A detectors ? What if you had four ? What about 5 ? How many detectors to you need to have the probability of protection to be 99 ? Now Sensor B is more sensitive. It can detect a chemical agent 75% of the time when an agent is present. What is the probability of protection If you have 3 Type B detectors ? What if you had four ? What about 5 ? How many detectors to you need to have the probability of protection to be 99 ? If you could only acquire 3 detectors of another type (not A or B), what would the probability of detection for this sensor have to be to have an overall protection probability of at least 99 % ?

Explanation / Answer

1) probability =1-P(none of 3 detect) =1-(1-0.75)3 =0.984375

2)probability =1-P(none of 4 detect) =1-(1-0.75)4 =0.996094

3)probability =1-P(none of 5 detect) =1-(1-0.75)5 =0.999023

4) from abvoe we can see that we need at least 4 detectors to have a probabilty of 99% .

a) let probabilty is p of detecting.

therefore probabilty of protection =0.99=1-(1-p)3

(1-p)3 =0.01

1-p=0.215

p=0.0.785

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