Maths question of the day

[djbaldken]

Odds are 1 in 64

Everyone seems to have forgotten one important premise. If there s 64 balls then for the first time it's 1 in 64. The second draw now has 62 balls. Therefore this time the odds are 1 in 62. Ergo the following draw now has 60 balls. So this time the odds are 1 in 60. Repeat until two balls remain. Then it's an even chance.
I don't have a degree in statistics, so could be wrong.

 

[PokerBlade]

Everyone seems to have forgotten one important premise. If there s 64 balls then for the first time it's 1 in 64. The second draw now has 62 balls. Therefore this time the odds are 1 in 62. Ergo the following draw now has 60 balls. So this time the odds are 1 in 60. Repeat until two balls remain. Then it's an even chance.
I don't have a degree in statistics, so could be wrong.

The odds of being a home draw means you need to be in 1 of the 32 "first" balls on each round. That's 32 opportunities to be drawn at home out of 64 possible positions. So 32/64, more commonly known as 1/2.

 

[Ball_Sup (Phil)]

Everyone seems to have forgotten one important premise. If there s 64 balls then for the first time it's 1 in 64. The second draw now has 62 balls. Therefore this time the odds are 1 in 62. Ergo the following draw now has 60 balls. So this time the odds are 1 in 60. Repeat until two balls remain. Then it's an even chance.
I don't have a degree in statistics, so could be wrong.

Last two balls are not perfectly even chance, as the two balls will not be uniform, one will be heavier, one lighter, due to completely impossible to manufacture two balls to be perfectly, exactly the same & unbiased. I do have two Degrees in Statistics, I'm wrong....

 

[djbaldken]

The odds of being a home draw means you need to be in 1 of the 32 "first" balls on each round. That's 32 opportunities to be drawn at home out of 64 possible positions. So 32/64, more commonly known as 1/2.

Pokerblade. You are missing my point. Each time two balls are drawn out the odds of being the next first ball get lower. It s not 64 positions each time. The positions lower by two each time.

 

[I should coco]

I think you'd have to throw* the cat to achieve this effect.

*Or ballistically launch

Our two permanently starving Tripe Hounds, are able to chase cats at such inter-galactic speeds, that a cat can be launched into a permanent rotating orbit at a height of approx 1.5m above sea level.

Fact!

(Unless it is a confident cat that stands it's ground. In that case, the two aforesaid fearsome hounds lightly whistle and pretend they haven't seen it, as they saunter on by).

 

[Sabella's Socks]

Last two balls are not perfectly even chance, as the two balls will not be uniform, one will be heavier, one lighter, due to completely impossible to manufacture two balls to be perfectly, exactly the same & unbiased. I do have two Degrees in Statistics, I'm wrong....

This is fun.

Taking it up/back a level, aren't the teams assigned different numbers at least each season, and possibly each round, so in the end it's still evens.

 

[Sabella's Socks]

While we're at it:

(1) Mr Currie has two children. The older child is a girl. What is the probability that both children are girls?
(2) Mr Woodward has two children. At least one of them is a boy. What is the probability that both children are boys?

 

[PokerBlade]

Pokerblade. You are missing my point. Each time two balls are drawn out the odds of being the next first ball get lower. It s not 64 positions each time. The positions lower by two each time.

What difference do you think this makes?

 

[1973Blade]

There's more chance of Elvis marrying Princess Diana on the moon, with Shergar as best man, than United getting a seventh consecutive League Cup home draw later on today. Awaits the forum statistics experts correcting me.

 

[Punk Blade]

Pokerblade. You are missing my point. Each time two balls are drawn out the odds of being the next first ball get lower. It s not 64 positions each time. The positions lower by two each time.

Ooh, another probability thread that I somehow missed at the time! Looks like this wasn’t resolved...

If you want to go down that route, you’ll have to calculate the probability of being drawn first or third or fifth... or sixty-third and add them all together. To calculate the probability of being drawn exactly third, for example, you would calculate the probability of not being drawn first, not being drawn second and then being drawn third: 63/64 x 62/63 x 1/62. Each position will come to 1/64. There are 32 home positions so adding together you’ll get 32/64. It’s just a very long-winded way of getting 1/2.

 

[SufcBilly]

Is everyone forgetting that’s it’s split into north and south so less teams for our group so it’s more likely?

 

[1973Blade]

We played Burnley away last season (when fans were not allowed anyway so it didn't really matter). However, we have now drawn Carlisle and Derby at home in the League Cup, which makes it 8 out of the last 9 matches that we have played at home in the competition. A little frustrating for those who would prefer to see us play at a new ground (eg Barrow) rather than a home time with most of the stands not open!

 

[Panini]

We played Burnley away last season (when fans were not allowed anyway so it didn't really matter). However, we have now drawn Carlisle and Derby at home in the League Cup, which makes it 8 out of the last 9 matches that we have played at home in the competition. A little frustrating for those who would prefer to see us play at a new ground (eg Barrow) rather than a home time with most of the stands not open!

25/8/15 was the last time we took an away following to a League Cup game, a 3-0 loss at Fulham. We'd won at Morecambe in the previous round.

 

[1973Blade]

25/8/15 was the last time we took an away following to a League Cup game, a 3-0 loss at Fulham. We'd won at Morecambe in the previous round.

Not good for those of us who would like to do the 92 grounds!

 

[1973Blade]

Now nine of the last ten league cup matches we have drawn at home.