National Lottery Dream Number odds

[198x]

How do the National Lottery get their odds for this game?

There are 7 chambers each with 10 balls (0-9) and so the probability should be 1 in 10.

However, the National Lottery quote that there's a 1 in 12 chance of getting the first number. How did they get these odds ?

[dzug]

It's 1 in 11.12 on their web site in the small print.

I would guess the explanation is it's the odds of winning �2 - they do say that the prize can be less depending on the number of entrants - not the odds of winning at all.

[Buenchico]

As you state, the probability of the first number matching is indeed 1 in 10 (i.e. 0.1) but some of the tickets which have the first number matching will also have the second number matching. Some of these will also have the third number matching, and so on.

You only win exactly �2 if the first number matches AND the second one doesn't. (Because of the way the game is structured, it doesn't matter what happens after a non-matching ball is drawn). The probability of a 'match' followed by a 'non-match' is 1/10 x 9/10 = 9/100. So the probability of getting a �2 prize should be 0.09, which is actually closer to 1 in 11 than it is to 1 in 12!

Chris