Probability conundrum Good morning, 
wondered if you could help me please?
I would like to work out the probability of and event happening 5 times out of 6.
all 6 events have a 1 in 60 chance of a particular outcome. I would like to know what the probability is when the event happens 6 times, and 5 of which have the same outcome.
if you could help it would be appreciated.
Thanks
Neil

Your situation correspond to binomial distribution with parameters $n=6$ and $p=1/60$ where each of 6 trials can have 60 possible outcomes.
First, let us focus on the $i$th term of the binomial expansion that corresponds that one fixed outcome (say $1$) occurs
$$
{{n}\choose{i}}p^i(1-p)^{n-i}
$$
Specifically:
$$
{{6}\choose{5}}\left(\frac{1}{60}\right)^5\frac{59}{60}
$$
Since each of the $n=6$ can have values $1,2,\dots 60$, we have to multiply this term by 60, i.e.
$$
{{6}\choose{5}}\left(\frac{1}{60}\right)^5 59
$$
