permutations/combinations question

[Gnevin]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

[thebigfella]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

Your not removing the cards after picking one and each event is independent, so it would make sense..... I could be wrong though 

[muppet]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

Clearly if you replace the card each time each draw is a new event. Therefore 20 goes would not be a 100% chance.

Think of rolling a dice.

It is not a 100% certainty that if you roll a di(c)e six times that you will hit the numbers 1,2,3,4,5 and 6 only once.

[Minus15]

Ahh there's a reason why I dropped out of Maths after 1st year

[Gnevin]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

Clearly if you replace the card each time each draw is a new event. Therefore 20 goes would not be a 100% chance.

Think of rolling a dice.

It is not a 100% certainty that if you roll a di(c)e six times that you will hit the numbers 1,2,3,4,5 and 6 only once.

Their is a difference between change and certainty if their is a 1 in 20 chance of something happening if you do it 20 times chances says it should happen but doesn't always have to.

http://www.random.org/playing-cards/?cards=1&decks=1&spades=on&hearts=on&aces=on&twos=on&threes=on&fours=on&fives=on&sixes=on&sevens=on&eights=on&nines=on&tens=on&remaining=on
20 card , start drawing for the 7 of hearts.

[thebigfella]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

Clearly if you replace the card each time each draw is a new event. Therefore 20 goes would not be a 100% chance.

Think of rolling a dice.

It is not a 100% certainty that if you roll a di(c)e six times that you will hit the numbers 1,2,3,4,5 and 6 only once.

Their is a difference between change and certainty if their is a 1 in 20 chance of something happening if you do it 20 times chances says it should happen but doesn't always have to.

http://www.random.org/playing-cards/?cards=1&decks=1&spades=on&hearts=on&aces=on&twos=on&threes=on&fours=on&fives=on&sixes=on&sevens=on&eights=on&nines=on&tens=on&remaining=on
20 card , start drawing for the 7 of hearts.

On that basis then 100% is not right as you can't be 100% certain a 7 will be drawn.

[Gnevin]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

Clearly if you replace the card each time each draw is a new event. Therefore 20 goes would not be a 100% chance.

Think of rolling a dice.

It is not a 100% certainty that if you roll a di(c)e six times that you will hit the numbers 1,2,3,4,5 and 6 only once.

Their is a difference between change and certainty if their is a 1 in 20 chance of something happening if you do it 20 times chances says it should happen but doesn't always have to.

http://www.random.org/playing-cards/?cards=1&decks=1&spades=on&hearts=on&aces=on&twos=on&threes=on&fours=on&fives=on&sixes=on&sevens=on&eights=on&nines=on&tens=on&remaining=on
20 card , start drawing for the 7 of hearts.

On that basis then 100% is not right as you can't be 100% certain a 7 will be drawn.

Their is a difference between chance and certainty . This is about the chance of something happening in a series of independent events. The chance of a 7 on any draw particular will always remain 1 in 20.

[Hound]

1-(1 - 1/20)^12 which I believe is 46% chance of it occurring if you only draw 12 cards.

As for 20,

1-(1 - 1/20)^20 = 64% chance it occurring.

That makes no sense if you draw 20 times the odds are 100% of getting one.

The answer for 20 is 64%.
If you did this exercisee 100 times, you would pick a 7 within 20 goes in close enough to 64 times - I bet.

100% chance (statistically), means it will definitely occur (it doesnt mean it should or might, it means it will). Which clearly is wrong.

[nifan]

Their is a difference between chance and certainty . This is about the chance of something happening in a series of independent events. The chance of a 7 on any draw particular will always remain 1 in 20.

There is but i dont think you understand the difference:)
100% chance means that it will always happen, no matter how often you run the test every time you draw 20 cards you will get a 7.

[full back]

If you draw a card & replace it then it is the same probability each time
You arent guaranteed to get a 7, no matter how may times you do it

[thebigfella]

If I have remembered correctly, calculating the probabilty a least one occurance of k independent events is calucaulated by

1 - (1 - α)^k

where each of the events has a probablity α of occuring. Thus you can't get 100%.

[A Quinn Martin Production]

I first thought that it had to be 20/1 as each event was independent but now I'm not so sure.  THe probablity that you will draw a seven is 20/1 for each event, so the probability that you would draw a seven on the first go is exactly the same for the 12th go.  A bit like if you toss a coin 25 times and get 24 tails in a row the probalbiltiy that you will get a tails on the 25th go?  2/1.  But here there area a fixed number of events.  So if we said there are two draws what are the chances of drawing a 7 in either draw?  The ans is not 20/1.  If you toss a coin 20 times what are the chances of tossing a tails at some point during the 20 events?  It's not 2/1...the chances are much greater than that...and that is the question that's being asked here...I think

[stpauls]

going to throw a spanner in the works here, are these 20 cards drawn randomly from a standard pack of 52 cards?
if so, you need to factor in the probability that there may not be a 7 in the deck of 20 drawn, or am i just being silly?

[muppet]

going to throw a spanner in the works here, are these 20 cards drawn randomly from a standard pack of 52 cards?
if so, you need to factor in the probability that there may not be a 7 in the deck of 20 drawn, or am i just being silly?

That's the leaving cert question. We are still at Junior Cert so our cards are numbered 1 - 20.

We should have started with a coin.

[stpauls]

going to throw a spanner in the works here, are these 20 cards drawn randomly from a standard pack of 52 cards?
if so, you need to factor in the probability that there may not be a 7 in the deck of 20 drawn, or am i just being silly?

That's the leaving cert question. We are still at Junior Cert so our cards are numbered 1 - 20.

We should have started with a coin.

probably would have been an easier question alright!!