A little maths teaser

[threebikesmcginty]

My favourite at the moment:

Chap takes the cellophane off a new pack of playing cards and thoroughly shuffles them. He then turns over the first card which is red and asks “what are the odds that the next card is also red”? The next card is indeed red and he asks again “what are the odds that the next card is also red”? He repeats this until remarkably he has turned over 6 red cards. When he asks the question again “what are the odds that the next (7th) card is also red” what is your answer ?

Is it referring to the colour of the back of the cards, they're all red?

 

[Thomk]

Is it referring to the colour of the back of the cards, they're all red?

Good point but no he's talking about whether it is a red card (hearts or diamonds) as opposed to black (spades or clubs).

 

[threebikesmcginty]

I don't care anymore...

 

[Maz]

No

Duff pack of cards.
Clearly been tampered with if it's brand new with no joker in it.

 

[Thomk]

Duff pack of cards.
Clearly been tampered with if it's brand new with no joker in it.

Not all decks of cards have jokers.

 

[Maz]

Not all decks of cards have jokers.

First 7 cards all red...
Probability =
[26/52] x [25/51] x [24/50] x [23/49] x [22/48] x [21/47] x [20/46]

 

[slowmotion]

As ever, 50% chance that it is red. It doesn't matter what happened previously.

 

[deptfordmarmoset]

First 7 cards all red...
Probability =
[26/52] x [25/51] x [24/50] x [23/49] x [22/48] x [21/47] x [20/46]

Ooh, I like that one. I'll go for your answer.

 

[thom]

My favourite at the moment:

Chap takes the cellophane off a new pack of playing cards and thoroughly shuffles them. He then turns over the first card which is red and asks “what are the odds that the next card is also red”? The next card is indeed red and he asks again “what are the odds that the next card is also red”? He repeats this until remarkably he has turned over 6 red cards. When he asks the question again “what are the odds that the next (7th) card is also red” what is your answer ?

Initially there were 52 cards. 26 red, 26 black.
You take out 6 red, so 20 of 46 are red in the remaining pile.
If these cards are well shuffled and uniformly random, the probability that the next card is red is 20 / 46 = 10 / 23.

 

[vernon]

2 pies....don't tell Vernon

Who said pies?

 

[Speicher]

About seven yards

 

[srw]

My favourite at the moment:

Chap takes the cellophane off a new pack of playing cards and thoroughly shuffles them. He then turns over the first card which is red and asks “what are the odds that the next card is also red”? The next card is indeed red and he asks again “what are the odds that the next card is also red”? He repeats this until remarkably he has turned over 6 red cards. When he asks the question again “what are the odds that the next (7th) card is also red” what is your answer ?

He was lying when he said he'd shuffled them thoroughly. It's another red card.

 

[srw]

I refer the honourable gentleman to the following post and subsequent replies.
Now we know where their questions come from ;-)

In fact the answer you'll have is slightly wrong on 2 counts:
1) the distance depends on the shape of the body - you reasonably assume the rope traces a circle round the earth for the purposes of the question but in reality, the peaks and dips in the earth invalidate this and the formula used - you need to know the exact description of the earth's surface where the rope lies
2) there is a small amount of curvature that even under the assumption that the earth is round, the distance between the two ends is just slightly less

Practically speaking, to a first approximation the answer will always be "considerably smaller than your intuition tells you it ought to be".
For instance you'd only need about an extra metre and a third to traverse Everest at a height of a metre (approximately modelling it as a triangle), so given the proportion of the earth's surface which is sea I'd guess the total extra is measured in the low hundreds of metres. On a total rope length of 40,000km that's almost nothing.

Mathematically the answer will depend, of course, on what fractal dimension you use to measure the earth. If you pick a high enough fractal dimension the answer could be infinite.

 

[Archie_tect]

Never mind the question, the idea of creating text that is the same colour as the background is brilliant....!

Brilliant!! I peeped...

 

[TVC]

Never mind the question, the idea of creating text that is the same colour as the background is brilliant. I can email folk and add a hidden postscript that says what I really think of them.
No peeping!

Good idea


Seriously, you need to get out more.