# Probability of all parts functioning

For a trip to be successfully launched, 100 different parts on the ship must all be functioning properly. The probability for each parts failing, $p$, is $0.0001$.

i. What is the probability that the trip will not be successful?
ii. What major assumption is made when calculating this probability?

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Hello, you must be new here. This looks like a homework question on probability. Why not you show us what you have thought about thus far, so we know how to help you? –  bryansis2010 Feb 7 '13 at 8:46

I will give some hints on this question -

This is very similar to a $x\space \text{-out-of-} \space n \space \text{reliablity}$ kinda question. I'd recommend you to consider the case where the trip is successful, where all the parts are functioning. This case will be, let's take the answer as $k$,

$$(1 - 0.0001)^{100} = k$$

Take $1-k$ and you get the probability that this trip will not be successful. In this case, you realize that you're using the complement of cases where 1 or more parts might fail...and this is actually an easier computation.

For your 2nd part, you have to assume that the event of 1 part failing is independent off all other parts failing. In the real case, if 1 part fails (say the deck), other parts will more likely to fail (the deck cover). This will directly affect the final outcome.

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As for the last paragraph, one may assume that the failure rates are given for the parts in isolation, i.e., under normal conditions. They do not take into account the possibility of say a nearby part exploding; that would make their failure rate almost meaningless (and in any case too high). So given that the question does not distinguish failure due to single or multiple calamities, I think the point you raise is irrelevant. –  Marc van Leeuwen Feb 7 '13 at 10:51
To put Marc's words in terms of probability, it's like saying the probability of 3 parts failing is dependent on the probability of 1 part failing (the explosion, affecting 3 parts). Marc, am I correct? –  bryansis2010 Feb 7 '13 at 14:14