Probability Question

[imported_adhoc]

I'd like to know how to calculate the probability of an event over a number of discrete trials with different likelihoods each time. This is probably simple, but I am not sure how to do it.

For instance, if the event has a likelihood of 45% in the first trial, 60% in the second trial, and 30% in the third trial, what is the overall likelihood it will happen over these three particular trials?

[Borodog]

The simplest way is to calculate the probability that is will not happen and subtract that from 1. So in your example, the probability of your event happening each successive trial is 45%, 60%, and 30%. So the probability of it not happening each successive trial is 55%, 40%, and 70%. The total probability of the even not happening during any trial is then .55 x .4 x .7 = .154, or 15.4%. Thus the probability of it occuring at some point in the 3 trials is then 84.6%.

[imported_adhoc]

Thanks Borodog.

My math is a little rusty, but don't you also have to subtract the probability of the event happening more than once?

In this case there are four ways this could happen. 1st & 2nd, 1st & 3rd, 2nd & 3rd, and 1st 2nd & 3rd.

[WhiteWolf]

[ QUOTE ]
My math is a little rusty, but don't you also have to subtract the probability of the event happening more than once?

In this case there are four ways this could happen. 1st & 2nd, 1st & 3rd, 2nd & 3rd, and 1st 2nd & 3rd.

[/ QUOTE ]

Borodog's method accounts for that automatically (which is why it is the prefered method, much simpler calculations).