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Oliver Sutton

What are the odds for this

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8 hours ago, Oliver Sutton said:

All 8 PL sides drawn apart in the last 16 of the FA Cup.

How would one work out the odds of that.

Fairly easily. But I can't type it on my phone.

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Imagine you have a bag with 8 red balls and 8 blue balls in it. You are going to take 8 balls from the bag. You want to know the odds that you will end up with only red balls.

There are 12,870 combinations of taking 8 objects from 16 (http://www.calculatorsoup.com/calculators/discretemathematics/combinations.php). Only one of these will give you 8 red balls.

Since you're interested in both the situations where you end up with only red balls or blue balls, the odds of either of these situations is 2/12,870 = 1/6435

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3 hours ago, Dorkins said:

Imagine you have a bag with 8 red balls and 8 blue balls in it. You are going to take 8 balls from the bag. You want to know the odds that you will end up with only red balls.

There are 12,870 combinations of taking 8 objects from 16 (http://www.calculatorsoup.com/calculators/discretemathematics/combinations.php)

Since you're interested in both the situations where you end up with only red balls or blue balls, the odds of either of these situations is 2/12,870 = 1/6435

It's a more complicated than that as there is no requirement for ALL premiership teams to be playing at home or away - some can be at home, others away.

The best way to work it out is just to play the draw out ball by ball.

That gives (8/15) * (7/13) * (6/11) * (5/9) * (4/7) * (3/5) * (2/3) * (1/1) which works out to about 1/50.

So, quite unlikely but something that most of us could expect to see in a lifetime.

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I love these probability tussles.

I think what can be deduced beyond all doubt is that probability must be one of the worst taught subjects in maths.

In calculus we either master it or come away knowing it just isn't for us. 

Probability? Yeah, I'll give it a go! Sure it might be maths, but we all have an opinion.

An opinion.  In maths. As if that were possible. How tf so?

Clearly this must be down to teachers instructing us falsely. How else could so many people think different things and all believe they are right?

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1 minute ago, Sledgehead said:

I love these probability tussles.

I think what can be deduced beyond all doubt is that probability must be one of the worst taught subjects in maths.

In calculus we either master it or come away knowing it just isn't for us. 

Probability? Yeah, I'll give it a go! Sure it might be maths, but we all have an opinion.

An opinion.  In maths. As if that were possible. How tf so?

Clearly this must be down to teachers instructing us falsely. How else could so many people think different things and all believe they are right?

The difference between this sort of probability and calculus is that the actual maths are easy, the difficulty comes from working out what the problem is.

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3 hours ago, Broken biscuit said:

It's a more complicated than that as there is no requirement for ALL premiership teams to be playing at home or away - some can be at home, others away.

The best way to work it out is just to play the draw out ball by ball.

That gives (8/15) * (7/13) * (6/11) * (5/9) * (4/7) * (3/5) * (2/3) * (1/1) which works out to about 1/50.

So, quite unlikely but something that most of us could expect to see in a lifetime.

Of course, that final statement of mine was complete cobblers since the fifth round draw doesn't always contain exactly 8 teams from the Premiership.

I still stand by my maths though which works out to 128 / 6435, or to put it another way, 1 in 50.2734 (to 4 decimal places).

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