Answer to Question #115083 in Statistics and Probability for Hs

Question

On 11 day in 10001000, there is a fire and the fire alarm rings.

On 11 day in 100100, there is no fire and the fire alarm rings (false alarm)

On 11 day in 10,00010,000, there is a fire and the fire alarm does not ring (defective alarm).

On 9,8899,889 days out of 10,00010,000, there is no fire and the fire alarm does not ring.

If the fire alarm rings, what is the (conditional) probability that there is a fire?

Written p(p(there is a fire | fire alarm rings))

Answer 1

p(there is a fire | fire alarm rings)=p( fire alarm rings and there is a fire)/p(fire alarm rings)

p( fire alarm rings and there is a fire)=11/10001000

p(fire alarm rings)=11/10001000+11/100100

p(there is a fire | fire alarm rings)=11/10001000/(11/10001000+11/100100)=0.0099