Mixing
Queen of Hearts Odds for weeks 1 - 54
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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 & week 54?
sequences-and-series
asked Jan 26 at 14:18
SJB1945SJB1945
1
$endgroup$
add a comment |
$begingroup$
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 & week 54?
sequences-and-series
asked Jan 26 at 14:18
SJB1945SJB1945
1
$endgroup$
add a comment |
$begingroup$
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 & week 54?
sequences-and-series
asked Jan 26 at 14:18
SJB1945SJB1945
1
$endgroup$
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 & week 54?
sequences-and-series
sequences-and-series
asked Jan 26 at 14:18
SJB1945SJB1945
1
asked Jan 26 at 14:18
SJB1945SJB1945
1
asked Jan 26 at 14:18
SJB1945SJB1945
1
asked Jan 26 at 14:18
SJB1945SJB1945
1
asked Jan 26 at 14:18
SJB1945SJB1945
1
1
add a comment |
add a comment |
1 Answer
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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?
answered Jan 26 at 15:44
PalePale
964
$endgroup$
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
add a comment |
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1 Answer
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1 Answer
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$begingroup$
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?
answered Jan 26 at 15:44
PalePale
964
$endgroup$
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
add a comment |
$begingroup$
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?
answered Jan 26 at 15:44
PalePale
964
$endgroup$
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
add a comment |
$begingroup$
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?
answered Jan 26 at 15:44
PalePale
964
$endgroup$
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?
answered Jan 26 at 15:44
PalePale
964
edited Jan 27 at 19:46
answered Jan 26 at 15:44
PalePale
964
answered Jan 26 at 15:44
PalePale
964
answered Jan 26 at 15:44
PalePale
964
964
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
add a comment |
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
That is the perfect phrasing for my question: how to determine the odds of not being drawn for any one week, e.g. week 34
$endgroup$
– SJB1945
Jan 27 at 15:20
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
$begingroup$
i just edited my answer, hope it helps!
$endgroup$
– Pale
Jan 27 at 19:46
add a comment |
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