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

• a maximum of 165,000 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
• 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 an equal chance of being drawn, meaning that there is a 1 in 165,000 chance of a specific ticket number being drawn.

In any single draw, each ticket number has a 164,999 in 165,000 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.

11,384 prize draws would be necessary and this would produce a probability of failure which is 0.9333321. This means that the probability of “success”, the complement of this failure probability, would be 0.0666679, which is 1 in 14.99970, slightly more favourable than the required 1 in 15.