(b) To reduce costly shutdowns caused by false alarms, management introduces a s
ID: 3064102 • Letter: #
Question
(b) 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?Explanation / Answer
We are given that each sensor gives a false alarm with probability = 0.02
The two sensors are independent of each other.
We are asked to calculate the probability that the reactor will shut down because of the simultaneous false alarms by both the first and second sensors.
Thus the required probability is:
Pr(false alrams on both the sensors) = Pr(false alarm on first sensor)*Pr(false alarm on second sensor)
[Because the two censors are independent]
=> Pr(false alrams on both the sensors) = 0.02*0.02 = 0.0004, which is the required probability.
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