In this lottery 5 balls are chosen from 1-50.
A friend offers me 5 to 1 if I can get one number correct from the 5 chosen, the order it comes up doesn't matter. Is this a good bet to take?
To get one number right I use this formula.
C(50,5)
-------------
C(5,1) × C(50-5, 5-1)
which gets me
2,118,760
--------------
744,975
That comes out to 2.844
TY
When you say you were offered $5:1$ I take that to mean that, for a $\$1$ bet you get handed $\$5$ PLUS you get your original $\$1$ back if you guess at least one of the correct numbers and that you simply lose your $\$1$ if you fail. Thus your potential profit is $5$ and your potential loss is $1$. Is this correct?
Assuming I have the question right, then we need the probability $p$ of guessing one right. Of course we have $$p=\frac 5{50}=\frac 1{10}$$
Thus your expected profit is $$E=5\times \frac 1{10}-1\times \frac 9{10}=-\frac 4{10}$$
As this is negative, you should avoid the bet.