Modern cars provide *blind-spot monitoring', a light which activates when an adjacent car is de- tected. Unfortunately, the system is not perfect. Given that another car is in the blind spot, the blind-spot light is activated 99.9% of the time. However, the system accidentally activates even when another car is not in the blind spot, this occurs 3% of the time. Assume that another car is in one's blind-spot 2% of the time. i What is the probability that another car is actually in the blind-spot given the light is on? ii Given the blind-spot light is off, how often is another car in the blind-spot?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Modern cars provide *blind-spot monitoring', a light which activates when an adjacent car is de-
tected. Unfortunately, the system is not perfect. Given that another car is in the blind spot, the
blind-spot light is activated 99.9% of the time. However, the system accidentally activates even
when another car is not in the blind spot, this occurs 3% of the time. Assume that another car is
in one's blind-spot 2% of the time.
i What is the probability that another car is actually in the blind-spot given the light is on?
ii Given the blind-spot light is off, how often is another car in the blind-spot?
Transcribed Image Text:Modern cars provide *blind-spot monitoring', a light which activates when an adjacent car is de- tected. Unfortunately, the system is not perfect. Given that another car is in the blind spot, the blind-spot light is activated 99.9% of the time. However, the system accidentally activates even when another car is not in the blind spot, this occurs 3% of the time. Assume that another car is in one's blind-spot 2% of the time. i What is the probability that another car is actually in the blind-spot given the light is on? ii Given the blind-spot light is off, how often is another car in the blind-spot?
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