I run a Lottery syndicate for the UK lottery, and we play 30 lines per draw.
The odds of winning £10 (3 matching numbers) is deemed to be 1 in 56.7 (or 1/57 for the purposes of this question).
I'd loosely determined that the odds of getting 3 numbers from 30 lines was approximated as 1 in 2 (or 30/57) - firstly, is this correct?
Secondly, we recently played 30 lines and matched 3 numbers on two of those lines. I'd like to tell my syndicate how likely that was expressed as a fraction, but I can't work it out (or be sure it is correct).
1 / 56.7 = 0.0176366843
I'd always learned that the occurance of something happening AND something else happening is the multiple of the probabilities. So, 0.0176366843 x 0.0176366843 = 0.00031105263.
Is that correct, and if so, what is the nearest representation of this number as a fraction? The fact this calculation doesn't seem to take into account that 30 lines were played makes me think it is wrong.