Over the last few years I've taught myself programming, and recently started a quest to teach my self R.

After a short while I realised that I have a severe lack of mathematical knowledge so I've bought myself a few books on statistics and am working my way through them.

I've used the binomial probability formula for p(x) and calculated flipping heads x times out of 10, the total of all the outcomes always equals 100% and this makes sense to me.

I then went a bit off piste and decided to try and work out for myself the probability of me rolling a 1 on a dice x amount of times out of 50.

If I understand it correctly p = .167 and product of the formula looks like the below.

I would expect to see the probability a lot higher and the total of all the lines to = 1 but this is not the case.

Can any one point me in the right direction or show me where I have gone wrong?

Any help would be greatly appreciated.

Thanks in advance

Lewis