The probability that detector B goes off is 0.75
The probability of an event is known to be the likelihood or chance for an event to occur.
From the given information let consider:
- A = the time when detector A goes off, and
- B = the time when detector B goes off
Since one or both of them always goes off, then:
∴
Their complements will be zero, i.e.
Similarly, we are given that:
Then;
∴
The set probability for A will be:
P(A) = 1 - P(A')
P(A) = 1 - 0.35
P(A) = 0.65
Finally, the probability that detector B goes off can be computed as:
P(B) = P(A) P(B|A) +P(A') P(B|A')
P(B) = P(A) (1 - P(B|A')) + P(A') (1 - P(B'|A')
![\mathbf{P(B) = P(A) (1-\dfrac{P(A \ and \ B')}{P(A)}) +P(A') (1 - \dfrac{P(A' \ and B')}{P(A')})}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28B%29%20%3D%20P%28A%29%20%281-%5Cdfrac%7BP%28A%20%5C%20and%20%5C%20B%27%29%7D%7BP%28A%29%7D%29%20%2BP%28A%27%29%20%281%20-%20%5Cdfrac%7BP%28A%27%20%5C%20and%20B%27%29%7D%7BP%28A%27%29%7D%29%7D)
![\mathbf{P(B) = 0.65 (1-\dfrac{0.25}{0.65}) +0.35 (1 - \dfrac{0}{0.35})}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%28B%29%20%3D%200.65%20%281-%5Cdfrac%7B0.25%7D%7B0.65%7D%29%20%2B0.35%20%281%20-%20%5Cdfrac%7B0%7D%7B0.35%7D%29%7D)
P(B) = 0.75
Learn more about the probability of an event here:
brainly.com/question/25839839