Calculating probability that 3 events occur 1 after other

• MHB
• isaiahRoberts707
In summary, the overall probability of all three events occurring is 0.008% or 0.00008 as a decimal. This is calculated by multiplying the individual probabilities of each event occurring while taking into account the dependency between them.

isaiahRoberts707

Let's say we have 3 events that all have a certain chance of occurring. Each latter event occurring depends on if the prior event occurred based on the chance associated with it. For example, if Event #1 does not happen, Event #2 cannot happen. As such, if Event #2 doesn't happen, Event #3 cannot happen. The overall goal is to prevent ever getting to Event #3, but if you do make it to Event #3, what is the chance that it happens too?

Probability for each event:
Event 1: 0.5% chance of occurrence
Event 2: 2% chance of occurrence
Event 3: 20% chance of occurrence

What is the overall probability (as a percentage) that all of these events will occur?

I have tried applying the dependent event probability formula here, but I have found that it doesn't seem to work in this scenario.

If someone could even give me somewhere to start or some applicable formula, It would be greatly appreciated. Thank you!

That looks straight forward given what you wrote. There is a 0.5% chance A will occur so a 1.000- 0.005= 0.995 or 99.5% none of A, or B, or C will happen.

There is a 0.5% chance A WILL happen and then a 1- 0.02= 0.98 or 98% chance B will NOT happen. There is a (0.005)(0.98)= 0.0049 or 0.49% chance A only will happen. There is a 0.5% chance A will happen and then a 2% chance B WILL happen. In that case there is a 1- 0.20= 0.80 or 80% chance C will NOT happen. So there is a (0.005)(0.02)(0.80)= 0.00008 or 0.008% chance of A and B but not C.
Finally there is a (0.005)(0.02)(0.20)= 0.00008 or 0.008% chance that all three will happen.