How to calculate the probability of many events in series? I am trying to determine the correct method to calculate the probabilities of this problem: Assume a piece of dust is travelling through a tube made up of 5 sections. If the particle touches a wall, it will stick and not travel further. I want to determine the probability that the particle will pass through all sections of the tube without getting stuck. Assume I have already obtained the probabilities of the particle getting stuck in each section of the tube. What is the proper way to calculate the overall probability of the particle making it through all 5 sections without sticking? Assume the probability of sticking is about 0.02 for each section, although it varies slightly. My initial assumption was to add all the probabilities together as they seem to me to be mutually exclusive events. Is this correct?

Let $P(S_{i})$ = the probability of making it through a section.

The probability of making it through all the sections, assuming that each event is an independent one, is given by

$\prod_{i=1}^{5}P(S_{i})$ = $0.98^{5} = 0.9039$ (4s.f.)

Edit:

Also note, that mutually exclusive events, are events which cannot occur simultaneously. For example, obtaining a $2$ versus obtaining a $3$ on a dice roll are mutually exclusive events. In this case, your events are independent ones. This means that the outcome of one event does not affect the outcome of another event, or more precisely:

$P(A|B) = P(A)$

where $P(A|B)$ denotes the probability of $A$ given $B$