Calculating probability that 3 events with certain percent chances are all met

[isaiahRoberts707]

Hey all,

I'm not too great at math, and I have a real-world math problem for you.

Let's say we have 3 events that all have a certain chance of occurring. Each latter event is dependent on if the earlier 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 event 3.

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?

What I have tried:
Nothing so far because I greatly struggled with statistics in earlier school, and it's been a while since I had anything like this. If someone could give me some sort of formula to try, I can write it up and post my work.

Thank you!

 

[isaiahRoberts707]

To add on: I've tried using dependent events conditional probability, but I've found that it doesn't exactly work in this scenario. No formula that I have found seems to work for this case.

 

[Dr.Peterson]

Hey all,

I'm not too great at math, and I have a real-world math problem for you.

Let's say we have 3 events that all have a certain chance of occurring. Each latter event is dependent on if the earlier 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 event 3.

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?

What I have tried:
Nothing so far because I greatly struggled with statistics in earlier school, and it's been a while since I had anything like this. If someone could give me some sort of formula to try, I can write it up and post my work.

Thank you!

To add on: I've tried using dependent events conditional probability, but I've found that it doesn't exactly work in this scenario. No formula that I have found seems to work for this case.

Please show us what you did, rather than just describe it. How do you know it didn't work?

As I understand it, event 1 happens 0.5% of the time; event 2 happens 2% of those times; and event 3 happens 20% of those. Just multiply, which I assume is what you did.

 

[Steven G]

The overall goal is to prevent event 3.
What is the overall probability (as a percentage) that all of these events will occur?

Which of the two above probabilities are you looking for?

 

[Steven G]

For me, it is not clear when you say:
Probability for each event:
Event 1: 0.5% chance of occurrence
Event 2: 2% chance of occurrence
Event 3: 20% chance of occurrence

2% of the time event 2 does happen.
You claim that event 3 can't happen if event 2 doesn't happen. So how can event 3 happen 20% of the time?