What you calculated is the probability that the first four events succeed and the last fails. You have to sum to that the probability that the one that fails is the first, then the second and so on. So you have:
0.2*0.75*0.7*0.65*0.6 + 0.8*0.25*0.7*0.65*0.6 + 0.8*0.75*0.3*0.65*0.6 + 0.8*0.75*0.7*0.35*0.6 + 0.8*0.75*0.7*0.65*0.4
if I didn't make any typo. In total you get about 36.315%.
The calculation in R:
Code:
probs<-c(0.80, 0.75, 0.70, 0.65,0.60)
sum(prod(probs)/probs*(1-probs))
#[1] 0.36315
