Probability calculation/PoS in a research project

Simi

New Member
Dear all,

as part of a project, I need to calculate some probabilities and would like to know whether my approach is fine The case is as follows:

In the research project, the following probabilities of success (PoS) for the transition from one phase to the other are known:

PoS of Ph 1: 60%
PoS of Ph 2: 35 %
PoS of Ph 3: 65 %
PoS of Ph 4: 70%
PoS of Ph 5: 40%

1) In order to determine the average probability of getting into Ph5, assuming the research project is carried out once, one would need to calculate: 60%*35%*65%*70%, right?

2) If one wants to find out the probability of failing at phase 3, one would need to calculate: 60%*35%*(100%-65%), correct? It would not be correct to calculate 60%*35%*(100%-(60%*35%*65%)), right?

3) Assuming the project is carried out five times, one would need to multiply with 5, right? (The reasoning is that with more projects the probability of finding a successful molecule is (on avergage) higher). So for example regarding 1) 5*60%*35%*65%*70% (Ph5) respectively 2) 5*60%*35%*(100%-65%).

4) How does one calculate the probability of finding not just 1, but 2 usable molecules if the project is carried out x times? I thought maybe the binomial coefficient has to be used. In Excel, for example, the following would have to be calculated for a project carried out 5 times P(2) = Binom.Dist(2(Number of successes),5(Experiments carried out),60%*35%*65%*70%*40% (Probability of success),False) = Percentage that two usable molecules are found. However, when performing this calculation for each phase 1-5, "strange" results emerged in my real life case: For example, the calculated probability of finding 2 usable molecules was lower up to Ph1 (successful completion of Ph 1) than up to Phase 2 (successful completion of Ph1 & Ph 2), etc. This does not seem right to me. Rather I would have expected, just like in the calculation for one molecule, that the PoS decreases, since an additional phase is added in every step. Do you have any idea what I am doing wrong?

5) How would I need to modify the calculation in 4) if I want to calculate the probability of finding two successful molecules in a row? Is the following calculation for Ph 2, correct: 60%*35%*60%*35%?

It's probably not complex, but I'm kind of stuck.

Thank you very much
Simi