A house has two identical sprinkles and humidity sensors that will trigger in: -

ID: 2930338 • Letter: A

Question

A house has two identical sprinkles and humidity sensors that will trigger in:

- 80% of the cases where the humidity is low

-15% of the cases where the humidity is nominal

- 0.5% of the cases where the humidity is high.

The probability of high humidity is 10%, nominal humidity is 50%, and low humidity is 40%.

Describe a Bayesian approach and corresponding queries for computing the following:

1) Probability that the first sprinkler will activate given that the other sprinkler was also activated

2) Probability that the humidity is low given that all both sprinklers are active

3) Probability that the humidity is low given that at least one sprinkle is active

1) P(first will activate | second activates)

As the events are independent

0.8*0.4+0.15*0.5+0.005*0.1 =0.3955

P(Low humidity | sprinklers active) = 0.8 ,P(Both sprinklers active in low humidity) = 0.8*0.8 = 0.64

P(Low humidity |Least one sprinklers active)=1- P(Low humidity |none sprinklers active) 1- 0.2*0.2

= 0.96

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