# What is the probability of success given two trials with a 1/16 chance each?

I have never been able to wrap my head around probability, and I often find that my intuition is wrong. In this case, I don't even have intuition as to where to begin.

If I have two trials, each with a 1/16 chance of success, what are the chances that either or both of them result in success? How, mathematically, do you arrive at the correct probability? How, intuitively, can I understand this number?

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The event you're interested in is the complement of the event that both trials fail. The chance of one trial failing is $1-1/16=15/16$, so the chance of both trials failing is $(15/16)*(15/16)=225/256$. So the chance of the opposite happening, which is what you're interested in, is $1-225/256=31/256$. – joriki Apr 6 '11 at 13:32
To help your intuition: what is the probability of a failure if you have one trial? if you have two trials? – Did Apr 6 '11 at 13:33
@joriki Why is that a comment and not an answer? – StrixVaria Apr 6 '11 at 13:33
The probability that neither trial is successful is $(15/16)^2$ (assuming that the trials are independent), and the chances that at least one trial is successful is one minus that: $1-(15/16)^2 = 31/256$.