A house security system uses two devices, A and B. If an emergency happens, the probability...

A house security system uses two devices, A and B. If an emergency happens, the probability that it will be detected by device A is 0.78; and by device B, 0.86; and by either device A or device B or both, 0.96. Determine the probability that an emergency will be detected by device A given that it is detected by device A. Write your answer in percent with 2 decimal places.

Expert Solution

P(A)=0.78

P(B)=0.86

P(A or B)=0.96

P(A and B)=P(A)+P(B)-P(A or B)=0.78+0.86-0.96=0.68

P(B|A)=P(A and B)/P(A)=0.68/0.78= 0.8718

orchestra answered 2 years ago

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