Question

To reduce costly shutdowns caused by false alarms, management introduces a sec- ond completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports o excessive radiation should be viewed as false alarms and ignored, since both sen- sors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors?

Answer 1

Answer:

a) 0.03

b) 0.0004

c) 0.0001

Step-by-step explanation:

Probability that the sensor reports what is going on accurately = 0.97

Probability that the sensor gives a false alarm = 0.02

Probability that the sensor gives a miss = 0.01

(a) Probability that the sensor reports what is going on accurately = 0.97

Probability that the sensor will give incorrect report = 1 - 0.97 = 0.03

It could also be evaluated as the probability that the sensor gives either a false alarm or gives a miss = 0.02 + 0.01 = 0.03.

b) Probability of false alarms on one sensor = 0.02

Since the two sensors are independent of each other,

The probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors

= 0.02 × 0.02 = 0.0004

c) Probability of a miss with one sensor = 0.01

Since the two sensors are independent of each other,

The the new probability that excessive radiation will be missed simultaneously by both the first and second sensors

= 0.01 × 0.01 = 0.0001

Hope this Helps!!!