Go figure this out! - Page 2

BeeJay55 · 20th January 2011, 21:27

This appears strange because there is the contrast between what they thought they had paid, and what they actually paid.

GT Courier · 20th January 2011, 21:31

Quote:

Originally Posted by BeeJay55

This appears strange because there is the contrast between what they thought they had paid, and what they actually paid.

You are right, it is more in the wording as the paid £30 and got £3 back thus £9 each...

GT Courier · 20th January 2011, 21:32

Quote:

Funny things, numbers.

Two football teams and a ref. on the pitch. What chance is there of two people having the same birthday .

23 people. 365 days in the year.

5%-----10%-------More ???

Colvert.

This one I forget, but its more than you think...I think..

BeeJay55 · 21st January 2011, 06:11

I would guess there is about a 50% chance ?

COLVERT · 21st January 2011, 17:21

Quote:

Originally Posted by BeeJay55

I would guess there is about a 50% chance ?

Perfect !! Lol.

Seen this one before ???????

BeeJay55 · 22nd January 2011, 16:26

I have not seen this one exactly. However, I know that in a class of 30 pupils there is a 50/50 chance that two of them were born on the same date.

I can't remember the maths involved, but I might well give it some thought just to exercise the old grey matter !

BeeJay55 · 22nd January 2011, 17:43

OK, I have given it some thought and with a spreadsheet to check my calculations, I would suggest the following:

This is a calculation based on Probability.

A Probability lies between 0 (impossible) and 1 (certain), or 0% and 100%.

In this case there are only two possible outcomes. Either someone has the same birthday as another, or they do not have the same birthday.

If we call the probability of the first P1 and the probability of the second P2, then P1 + P2 = 1 , or 100%

If we ignore leap years, which seems to throw in an additional difficulty (ie it is every 4th year, not every year) we will first assume that in all years in question the number of days is 365.

So, if we take the first person in a group as a 'fixed point', ie we will see if anyone else has their birthday. We will look at the probability that the birthdays are NOT the same (the probability they are not the same, and the probability they are the same equals 1). It is just easier to calculate this way.

The chance that the second person has a DIFFERENT birthday to the first is very high, ie 364/365. The chance of a third person not having the same birthday as the first two people is 363/365 and so on.

If you calculate a series like this on a spreadsheet, and sum them as you go, you will find you get to 23 people the probability calculates to 46.2%

Therefore, if the probability that in a group of 23 people no two have the same birthday is 46.2%, the probability that any two people DO have the same birthday is 100% - 46.2% = 53.8%

All those evenings helping the kids with GCSE Maths were not wasted - I also learned a thing or two !

COLVERT · 22nd January 2011, 18:02

Yes, over 50% probability.

Person one can be paired with any of the remaining 22 people.
Person two can be paired with any of the remaining 21 people.
Person three--------------------------------------20 people'

And so on.

Giving a total of 253 pairs.

20th January 2011, 21:27	#11
BeeJay55 Avid contributor Rover 75 Tourer, Connoisseur SE Join Date: Nov 2010 Location: Welshpool Posts: 185 Thanks: 0 Thanked 1 Time in 1 Post	This appears strange because there is the contrast between what they thought they had paid, and what they actually paid. __________________ *I’m a dyslexic agnostic with insomnia… I lie awake at night wondering if there really is a dog!*

21st January 2011, 06:11	#14
BeeJay55 Avid contributor Rover 75 Tourer, Connoisseur SE Join Date: Nov 2010 Location: Welshpool Posts: 185 Thanks: 0 Thanked 1 Time in 1 Post	I would guess there is about a 50% chance ? __________________ *I’m a dyslexic agnostic with insomnia… I lie awake at night wondering if there really is a dog!*

22nd January 2011, 16:26	#16
BeeJay55 Avid contributor Rover 75 Tourer, Connoisseur SE Join Date: Nov 2010 Location: Welshpool Posts: 185 Thanks: 0 Thanked 1 Time in 1 Post	I have not seen this one exactly. However, I know that in a class of 30 pupils there is a 50/50 chance that two of them were born on the same date. I can't remember the maths involved, but I might well give it some thought just to exercise the old grey matter ! __________________ *I’m a dyslexic agnostic with insomnia… I lie awake at night wondering if there really is a dog!*

22nd January 2011, 17:43	#17
BeeJay55 Avid contributor Rover 75 Tourer, Connoisseur SE Join Date: Nov 2010 Location: Welshpool Posts: 185 Thanks: 0 Thanked 1 Time in 1 Post	OK, I have given it some thought and with a spreadsheet to check my calculations, I would suggest the following: This is a calculation based on Probability. A Probability lies between 0 (impossible) and 1 (certain), or 0% and 100%. In this case there are only two possible outcomes. Either someone has the same birthday as another, or they do not have the same birthday. If we call the probability of the first P1 and the probability of the second P2, then P1 + P2 = 1 , or 100% If we ignore leap years, which seems to throw in an additional difficulty (ie it is every 4th year, not every year) we will first assume that in all years in question the number of days is 365. So, if we take the first person in a group as a 'fixed point', ie we will see if anyone else has their birthday. We will look at the probability that the birthdays are NOT the same (the probability they are not the same, and the probability they are the same equals 1). It is just easier to calculate this way. The chance that the second person has a DIFFERENT birthday to the first is very high, ie 364/365. The chance of a third person not having the same birthday as the first two people is 363/365 and so on. If you calculate a series like this on a spreadsheet, and sum them as you go, you will find you get to 23 people the probability calculates to 46.2% Therefore, if the probability that in a group of 23 people no two have the same birthday is 46.2%, the probability that any two people DO have the same birthday is 100% - 46.2% = 53.8% All those evenings helping the kids with GCSE Maths were not wasted - I also learned a thing or two ! __________________ *I’m a dyslexic agnostic with insomnia… I lie awake at night wondering if there really is a dog!*

22nd January 2011, 18:02	#18
COLVERT This is my second home R75 Saloon. Join Date: Feb 2009 Location: France/or Devon. Posts: 14,003 Thanks: 3,851 Thanked 2,167 Times in 1,816 Posts	Yes, over 50% probability. Person one can be paired with any of the remaining 22 people. Person two can be paired with any of the remaining 21 people. Person three--------------------------------------20 people' And so on. Giving a total of 253 pairs.