Queen of Hearts Odds for weeks 1 - 54 The queen of hearts is a weekly drawing where one card is selected each week until the queen of hearts is exposed.  The cards (52 plus the two jokers) are randomly ordered and placed face down and are numbered 1 - 54.

Each week a "chance" is drawn from those players participating  That ticket has one of the "available" numbers.  The card  matching that number is turned over and if the queen of hearts is shown the game is over and the person whose chance was selected wins.

It is possible for the game to continue for 54 weeks, my question is what are the odds that the queen will be found in week 1, week 2, .. week 53 &amp; week 54?
I would suggest thinking about: "What are the odds that the Queen of Hearts hasn't been drawn in Week 34?" for example.

If you need more help, just let me know.

EDIT:

Let's just take week 35 as an example. It's the 35th drawing made, and the card hasn't been found in the 34 previous ones. Since it's week 35, there a still 20 cards left. The probability NOT to pick the Queen this week is $\frac{19}{20}$.

This then becomes a basic probability problem, where e.g. in week 35, you would have a

$\frac{53}{54}\frac{52}{53} ...\frac{20}{21}\frac{19}{20}$ % chance NOT to have drawn the Queen of Hearts at this time.

Can you figure out when the 50% chance mark is hit?
Obviously each week the queen of hearts is not picked your odds increase. I don't think that was the original question. Is it more likely to come up the 1st week or the 26th week or any other week. The answer is just as likely any week because your odds are 1/54. if it's not picked the 1st week, that's one of the 54 picks and each subsequent week is another of the 54 picks.