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rodikova [14]
3 years ago
12

The security system in a house has two units that set off an alarm when motion is detected. Neither one is entirely reliable, bu

t one or both always go off when there is motion anywhere in the house. Suppose that for motion in a certain location, the probability that detector A goes off and detector B does not go off is 0.25, and the probability that detector A does not go off is 0.35. What is the probability that detector B goes off?
Mathematics
1 answer:
Mariulka [41]3 years ago
5 0

Answer:

Probability that detector B goes off is '0.615'

Step-by-step explanation:

Given that:

1) Probability that detector A goes off and detector B does not go off is 0.25.

2)Probability that detector A does not go off is 0.35.

3)Probability that detector A  goes off is (1-0.35)=0.65

Assuming that

Probability that detector B goes off is 'p' Hence the probability that detector B does not goes off  is (1-p)

Thus the probability that detector A goes off and detector B does not go off is  product of the individual probabilities

P(E)=0.65\times (1-p)\\\\0.65\times (1-p)=0.25\\\\0.65-0.65p=0.25\\\\0.65-0.25=0.65p\\\\\therefore p=\frac{0.40}{0.65}=0.615

Probability that detector B goes off is '0.615'

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