Can You Calculate the Probability of an Event in a Dependent Outcome Scenario?

[Astro since 73]

Statistics question...

This may be very elementary to some of you folks so bear with me. I just found your site today and wanted to pose a question that has bothered me for a couple of years. I never took statistics in college so I'm sure that explains why.

Anyway...

If you are given Incident (I) and are told that there can be two possible outcomes to this incident (a) and (b).

Then you are told that if (a), there are two possible outcomes (c) and (d)

Then you are told that for every 100 occurrences of (I), a = 90 and b = 10

and for a = 90, c = 86 and d = 4

First of all I know that it is correct to say that a = 90% of I

it is also correct to say that c = 95.5% of a



What I wasnt to know is... since c is dependent on a, is it alright to say that c is 86% of I since c could not occur without a occurring first?

someone told me you could multiply the percentages 90% * 95.5% and that would be 85.9%. Is that allowable? Is that the correct way to describe probability?



If my problems statement is too obscure, please tell me and I will restate it a different way. I just wanted to do it 'generically'.

 

[FZ+]

Usually, probabilities are taken in terms of decimals (0 to 1) or fractions instead of percentages.

When you are taking the probabilities of separate events BOTH happening, then you multiply the probabilities.

However, in this case it is better to just consider the overall outcomes, as you have done. Ie. in this case, we have 3 outcomes (b) (c) and (d), and then we can divide one from the total.

 

[tacman]

To answer your question, yes, it is correct to say that c is 86% of I since c is dependent on a. This is because c cannot occur without a occurring first, as you mentioned. Multiplying the percentages of a and c (90% * 95.5%) is not the correct way to describe probability in this case. This is because the probability of c occurring is not solely based on the probability of a occurring, but also on the probability of b occurring. In this case, c is 86% of a, but only 8.6% of I (since b has a 10% probability). Therefore, the correct way to describe the probability of c occurring is to say that it is 8.6% of I. I hope this helps clarify your understanding of probability in this scenario.