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What are the chances....


Vespa Red

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Now, I'm no statistician.  However, I was having a discussion with my son this morning about the chances of drawing Man Utd at Old Trafford in tonights draw should (of course) they get beyond Burton tonight.  I thought that there was a 1 in 30 chance (1 in 15 that we draw them, 1 in 2 that it's away).  However, is the equation more complex than that (some of you may wish to factor in the probabilities of Man Ure getting past Burton, some of you probably couldn't give a shit)? 

In case you're wondering I'm having a slow work day, and my son is learning GCSE maths....

 

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Surely Man Utd being drawn out first to get a home tie is 8/16 or 1/2. City to be drawn away is also 1/2 also. To draw Man Utd at OT is 1/2 x 1/2 x 1/8 (only 8 ties), so a 1/32 chance?  We also gave by that maths a 1/32 chance of drawing them at home therefore a 1/16 chance of drawing them either home or away. 

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8 hours ago, Davefevs said:

Surely Man Utd being drawn out first to get a home tie is 8/16 or 1/2. City to be drawn away is also 1/2 also. To draw Man Utd at OT is 1/2 x 1/2 x 1/8 (only 8 ties), so a 1/32 chance?  We also gave by that maths a 1/32 chance of drawing them at home therefore a 1/16 chance of drawing them either home or away. 

 Not quite. Take the 1/16 chance of drawing them. There are only 15 other teams we can play not 16, as we cannot play ourselves, so there is a 1/15 chance of drawing them, the same as any other side. We must draw one of the other 15 sides.

It is then a conditional probability. If Man Utd is drawn at home (lets call that a 1/2 chance as you say) and we are taking that as a given, then there is not a 1/2 chance left of us being home or away. One of the home slots is taken. We then have a 7/15 chance of getting one of the other home slots, and a 8/15 chance of getting an away slot.

Using your logic, the odds of both happening are then 1/2 x 8/15 x 1/8 gives 8/240 which cancels to 1/30.

The quick way is to say its a 1/15 chance of drawing them. Given that, its a 50/50 either home or away, so the odds are 1/30.

I will be testing on this later...

 

 

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Random probability fact of the day for you to ponder.

The chances that anyone has ever shuffled a pack of cards in the same way twice in the history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is ‘52 factorial’ otherwise known as 52!. This is 52 times 51 times 50 . . . all the way down to one. 

If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles, statistically speaking.

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15 minutes ago, cityexile said:

 Not quite. Take the 1/16 chance of drawing them. There are only 15 other teams we can play not 16, as we cannot play ourselves, so there is a 1/15 chance of drawing them, the same as any other side. We must draw one of the other 15 sides.

It is then a conditional probability. If Man Utd is drawn at home (lets call that a 1/2 chance as you say) and we are taking that as a given, then there is not a 1/2 chance left of us being home or away. One of the home slots is taken. We then have a 7/15 chance of getting one of the other home slots, and a 8/15 chance of getting an away slot.

Using your logic, the odds of both happening are then 1/2 x 8/15 x 1/8 gives 8/240 which cancels to 1/30.

The quick way is to say its a 1/15 chance of drawing them. Given that, its a 50/50 either home or away, so the odds are 1/30.

I will be testing on this later...

 

 

Nice. :clap:

I was trying to keep it simple, didn’t want to get into the maths of the effect of what happens once one ball is pulled out.

Both of us are wrong though, because we’ve failed to factor in the probability of the draw being effed up, because it appears we can be drawn home and away in the same draw (Watford) :whistle:

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7 minutes ago, redsontour said:

For goodness sake, the odds are 50/50, we were teached that at school...

 

Sorry, scrub that, that was the odds of tossing heads & tails...

...or if you throw a fair coin 100 times there is only about an 8% chance you get 50 heads?

No? scenes.

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46 minutes ago, cityexile said:

...or if you throw a fair coin 100 times there is only about an 8% chance you get 50 heads?

No? scenes.

Oh FFS they told me 50/50, I can't break it down further than that..

What we need is an actuary...but then, to be honest, we would all lose the will to live before we had got to @Robbored giving his view on GJ and I am not prepared to accept that.

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