There is a 1 in 15 chance of winning in The Hospital Research Foundation Home Lottery!

• A maximum of 170,000 tickets will be sold and eligible to be drawn;
• One ticket number is drawn at a time, after each draw the winning ticket number is recorded and is re-entered into the drawing process, which means that a ticket can win more than one prize;
• Each ticket number is equally likely to be drawn in a single draw, regardless of whether it has already won one or more prizes; and
• There may be additional bonus draws which are available only to tickets purchased prior to certain dates.

In any single draw, each ticket number has a 169,999 in 170,000 chance of not winning a prize. For any single ticket to be “unlucky” in not winning a prize across all of the draws, this failure of probability needs to be compounded (or multiplied by itself) for the number of prize draws. If there is a 1 in 15 chance of winning a prize the chance of failure must be 14 in 15 (or 0.9333333) or less.

11,729 prize draws would be necessary and this would produce a probability of failure which is 0.9333320. This means that the probability of “success”, the complement of this failure probability, would be 0.0666680, which is 1 in 14.99970, slightly more favourable than the required 1 in 15.