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On 1 day in 1000, there is a fire and the fire alarm rings. On 1 day in 100, there is no fire and the

On 1 day in 1000, there is a fire and the fire alarm rings.

On 1 day in 100, there is no fire and the fire alarm rings (false alarm)

On 1 day in 10,000, there is a fire and the fire alarm does not ring (defective alarm).

On 9,889 days out of 10,000, there is no fire and the fire alarm does not ring.

If the fire alarm does not ring, what is the (conditional) probability that there is a fire?

Written "p(there is a fire | fire alarm does not ring)"

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