Answer to Question #4600 in Statistics and Probability for Jeff

Question #4600

If you are calculating the probability of being able to prevent the occurrence of an event and have already determined the following:

. Barrier 1 has a 50% chance of preventing the problem
. Barrier 2 has a 50% chance of preventing the problem
. Barrier 3 has a 75% chance of preventing the problem

What is the combined effect of all three barriers, with regard to probability of preventing the problem?

Looking at a "similarly different" problem, from the probability of occurrence of an event if:

. Barrier 1 reduces the likelihood of occurrence to 1 in 100 (0.01)
. Barrier 2 reduces the likelihood of occurrence to 1 in 1000 (0.001)
. Barrier 3 reduces the likelihood of occurrence to 1 in 10000 (0.0001)

What is the combined effect of all three barriers, with regard to probability of occurrence of the event?

Expert's answer

P = 0.01*0.001*0.0001 = 0.000000001
So, the all these barriers combined together reduce the likelihood of occurrence to 1 in 1000000000.