# calculating probability of success

I have question on success of a project. If a project has following probabilities for failure, what is the success probability for the project? failure probability year 1 0.3 year 2 0.6 Here is the solution. success = (1-0.3) * (1-0.6) = 0.28 = 28% failure = 100- 28= 72% What I can’t understand is if I multiply these probabilities directly to get for failure, I am getting different percentage as given below failure = .3*.6 = .18 = 18%

because you are not eliminating all the possibilities what you are calculating is the probability of the project failling in year one and year 2 ( which of course does not make sense) you calculate the probability of succeding first year and then the second one what you have left is probabilities of failing first year or the second one

instead you would have to calculate probability for failure first year 0.3 probability for failure 2nd year 0.7*0.6=0.42 cause has to bee succesful first year to be able to be unsuccesful 2nd year the you add them up 0.72