permutations/combinations question

[thebigfella]

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?

Think of it this way, you have a bag of 20 marbles, each number 1 to 20. Each marble is then replaced after each draw and thus each draw is independent of each other.

In your example, you have 2 mutually exclusive events, "if 20 cards are drawn from a deck and none are a 7, then you cannot draw a 7 from the 20". Might have to go get the old GCSE text books out 

[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?

Think of it this way, you have a bag of 20 marbles, each number 1 to 20. Each marble is then replaced after each draw and thus each draw is independent of each other.

In your example, you have 2 mutually exclusive events, "if 20 cards are drawn from a desk and none are a 7, then you cannot draw a 7 from the 20". Might have to go get the old GCSE text books out 

this is more like an a level question so will have to see if those books are still lying about somewhere!! 

[thebigfella]

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?

Think of it this way, you have a bag of 20 marbles, each number 1 to 20. Each marble is then replaced after each draw and thus each draw is independent of each other.

In your example, you have 2 mutually exclusive events, "if 20 cards are drawn from a desk and none are a 7, then you cannot draw a 7 from the 20". Might have to go get the old GCSE text books out 

this is more like an a level question so will have to see if those books are still lying about somewhere!! 

I done Advanced Maths at GCSE 

[Treasurer]

After a bit of searching through maths books admiittedly,  I'm getting the same result as bigfella, ie 46%      

1st pick, 95% chance of not picking the card (think we're all agreed there!)      
2nd pick - on its own is again a 95% but multiply this by the first 95% to calculate chance over the 2 cards = 90.25%      
3rd pick, multiply the 90.25% by a further 95% and so on      

So....      

Pick No  Chance it Won't Happen     Chance It Will
1 pick      0.95                                         5%
2            0.9025                                    10%
3            0.857375                                14%
4            0.81450625                             19%
5            0.773780938                           23%
6            0.735091891                           26%
7            0.698337296                           30%
8            0.663420431                           34%
9            0.63024941                             37%
10           0.598736939                           40%
11           0.568800092                           43%
12           0.540360088                           46%

[thebigfella]

After a bit of searching through maths books admiittedly,  I'm getting the same result as bigfella, ie 46%      

1st pick, 95% chance of not picking the card (think we're all agreed there!)      
2nd pick - on its own is again a 95% but multiply this by the first 95% to calculate chance over the 2 cards = 90.25%      
3rd pick, multiply the 90.25% by a further 95% and so on      

So....      

Pick No  Chance it Won't Happen     Chance It Will
1 pick      0.95                                         5%
2            0.9025                                    10%
3            0.857375                                14%
4            0.81450625                             19%
5            0.773780938                           23%
6            0.735091891                           26%
7            0.698337296                           30%
8            0.663420431                           34%
9            0.63024941                             37%
10           0.598736939                           40%
11           0.568800092                           43%
12           0.540360088                           46%

So based on the same rule used to work out the probablity for 12 independent events, apply it to 20 and the answer is 64% (to the nearest %  ).

[scud]

This is slightly off topic but would help me settle an old discussion 

Say a couple have seven children, all girls. Base this on the premise that the chances of boy/girl are 50/50 each time. Am I right in saying that the overall chances of having 7 girls is 0.004%?

But each event, excluding any biological/physiological factors that may skew the probability, is still 50/50?

[Rossie11]

I would have it at 0.0078%

(1/2) to power of 7

[Bogball XV]

This is slightly off topic but would help me settle an old discussion 

Say a couple have seven children, all girls. Base this on the premise that the chances of boy/girl are 50/50 each time. Am I right in saying that the overall chances of having 7 girls is 0.004%?

But each event, excluding any biological/physiological factors that may skew the probability, is still 50/50?

I know this isn't what you're asking, but afaik the probablility of having a girl is actually less than 50, it's something like 49% - don't ask me why though.

[muppet]

This is slightly off topic but would help me settle an old discussion 

Say a couple have seven children, all girls. Base this on the premise that the chances of boy/girl are 50/50 each time. Am I right in saying that the overall chances of having 7 girls is 0.004%?

But each event, excluding any biological/physiological factors that may skew the probability, is still 50/50?

I know this isn't what you're asking, but afaik the probablility of having a girl is actually less than 50, it's something like 49% - don't ask me why though.

Men (historically) more likely to die before reproduction?

[Franko]

I would have it at 0.0078%

(1/2) to power of 7

Agreed - 0.00078 is the correct answer.

[Bogball XV]

This is slightly off topic but would help me settle an old discussion 

Say a couple have seven children, all girls. Base this on the premise that the chances of boy/girl are 50/50 each time. Am I right in saying that the overall chances of having 7 girls is 0.004%?

But each event, excluding any biological/physiological factors that may skew the probability, is still 50/50?

I know this isn't what you're asking, but afaik the probablility of having a girl is actually less than 50, it's something like 49% - don't ask me why though.

Men (historically) more likely to die before reproduction?

Yeah, would imagine it's evolution working its wonders again.

Look at these figures from Russia:

0-14 years: 14.8% (male 10,644,833/female 10,095,011)
15-64 years: 71.5% (male 48,004,040/female 52,142,313)
65 years and over: 13.7% (male 5,880,877/female 13,274,173) (2009 est.)

[Maiden1]

This is slightly off topic but would help me settle an old discussion 

Say a couple have seven children, all girls. Base this on the premise that the chances of boy/girl are 50/50 each time. Am I right in saying that the overall chances of having 7 girls is 0.004%?

But each event, excluding any biological/physiological factors that may skew the probability, is still 50/50?

I know this isn't what you're asking, but afaik the probablility of having a girl is actually less than 50, it's something like 49% - don't ask me why though.

Men (historically) more likely to die before reproduction?

Yeah, would imagine it's evolution working its wonders again.

Look at these figures from Russia:

0-14 years: 14.8% (male 10,644,833/female 10,095,011)
15-64 years: 71.5% (male 48,004,040/female 52,142,313)
65 years and over: 13.7% (male 5,880,877/female 13,274,173) (2009 est.)

Not sure about Russia but in countries like India and China the male to female live birth ratio (6:5) is much more skewed towards male children.  More to do with aborting female children than anything evolutionary.

[magpie seanie]

Loved these sort of questions at school. A bit rusty now though.

[A Quinn Martin Production]

Reminds me of the one I once read...if there are thirty people in a room what are the chances that two of them share the same birthday (i.e. the same date but not the same year)?  Can't remember the exact anwer but it's higher than you might at first think.

[David McKeown]

I always enjoyed things like this too.  Derren Brown talks alot about this sort of thing in one of his books and its quite interesting.  The one I used to like to use with people was the three door prize.  Say you are on a game show and at the end you get to choose from three doors to win a prize.  Behind one door is the prize.  Behind the other doors are booby prizes.  You pick a door, the game show host then opens one of the other doors to reveal a booby prize.  The host then asks you would you like to change your door.  Should you change?  This appeared in 21 there last year