Probability of undesirable outcome...?

[clerkind]

Hi all,

I'm an office based scientist with a work related quandary that I'm trying to wrap my head around .

I have to provide some indication of risk for a project.

The project will entail undertaking 3 separate studies on 3 different test materials. The studies can be either positive for genotoxicity or negative for genotoxicity. I have estimated that any one particular study has an 80% chance of being negative for genotoxicity (a desirable result) and I’m trying to estimate the probability of any one of these studies as being positive for genotoxicity.

The equation I’ve used is to multiple the probability of a negative genotoxic outcome: 0.8 x 0.8 x 0.8 = 0.5 (or 50%).

Does anyone know if this is the correct calculation methodology to employ in this context? It seems generally intuitively correct, but intuition isn’t always the best yardstick in mathematics I'd imagine.

Any assistance gratefully received,

Kind regards
David

 

[tkhunny]

Are they independent trials? Each has no relationship to the other? You have calculated the probability that ALL THREE will be negative.

There are 8 possible outcomes. Account for all 8.

Neg, Neg, Neg ==> .8*.8*.8
Neg, Neg, Pos ==> .8*.8*.2
Neg, Pos, Neg ==> .8*.2*.8
Neg, Pos, Pos ==> .8*.2*.2
Continue...

Add up all the ones with ANY negative result.

Alternatively, you could realize that the probability of ANY ONE being negative is the same as ONE MINUS the probability that ALL are positive. Thus: 1 - .2*.2*.2 = 99.2%

I'll send you the consulting bill.

 

[clerkind]

Hey thanks

Thanks for the response tkhunny and great name by the way.

Yes the tests are independent.

The probability values I'm after are:

I) Probability that all three are negative.
ii) Probability that any single test is positive (we don't care which one).

I'd welcome some more of your statistical prowess to confirm (or not) the values in those two scenarios.

Kind regards
David

 

[ksdhart2]

Also, uh, 0.8³ is not 0.5. It's actually 0.512. If you want to round to two decimal places, so as to report an integer percentage, it would be 0.51 = 51%.