Event Probability

[Orion]

Hi, I need help to find out how to do this problem im stumped

"Theres a 20% chance of Event A happening, if you try X number of times(lets say 6) whats the probability of Event A happening atleast once?"

I've tried to figure it out myself but im not sure if its right, all i did was 10(.2x6) based off an example on another site that wasnt very explanitory :?

 

[galactus]

The best thing to do with an 'at least once' problem, is to find the probability of none and subtract from 1.

The problem of the event not happening is .80.

We can use a binomial and do it this way. \(\displaystyle 1-(.20)^{0}(.80)^{x}\)

That would be the probability of it happening at least once because we found the probability of it not happening and subtracted from 1. Now, let's give x a number. We'll go with 6 since that is what you had in your example.

\(\displaystyle 1-(.2)^{0}(.8)^{6}=.737856\)

or, we could just add up all the cases from 1 to x. In this case 1 to 6. And get the same thing.

\(\displaystyle \sum_{k=1}^{6}C(6,k)(.2)^{k}(.8)^{6-k}=.737856\)

That is why we usually subtract the 'none' case from 1 because it is easier than counting up all the cases from 1 to x. Especially, if x is big. If it were, say, 100 we wouldn't want to add all that, would we?.

Think about why we do that. If we have at least one, it means we have something. From the bare minimum up to x. What's left?. None.



Google binomial probability and you'll find lots.

See now?.

 

[Orion]

Thanks alot, especially for the fast reply