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Vespa Red

What are the chances....

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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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I believe the odds are 1 in 30 x 1 in 29.

If 2 other teams get drawn first it'll be 1 in 28 x 1 in 27 and so on.....

Edited by Nomad

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18 minutes ago, Vespa Red said:

As there are only 16 teams left in the draw tonight, wouldn't that be 1 in 15 x 1 in 14?

correct

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It is 1 in 30. There are 15 possible home matches and 15 possible away matches.

1/16 (Man Utd drawn first) multiplied by 1/15 (Bristol City drawn second) are the odds that it is the first tie drawn out.

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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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If the draw is unseeded, we have an equal chance of drawing any one of the other 15 clubs in the draw, thus our chances of drawing Man U is 1/15.  There is a 1/2 chance that if we do draw them it will be at home, so there is a 1/30 chance of drawing Man U at home.

Edited by Malago

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1 hour ago, Vespa Red said:

As there are only 16 teams left in the draw tonight, wouldn't that be 1 in 15 x 1 in 14?

 

 

 

Was what I meant...... Just saw the 30 and assumed 30 teams. My bad. Especially as it would have been 32 :facepalm:

Edited by Nomad

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The odds on us drawing Gillingham away are probably 2/1 and that's even though Gills are not in the draw!

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Waht are the odds that we draw ourselves? Now that's a game I would like to see at the moment, our "Tuesday team" V our "Weekend team" :) 

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5 minutes ago, Port Said Red said:

Waht are the odds that we draw ourselves? Now that's a game I would like to see at the moment, our "Tuesday team" V our "Weekend team" :) 

The way the draws have been handled in this shambolic cup, quite high.

Edited by RumRed
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5 minutes ago, Port Said Red said:

Waht are the odds that we draw ourselves? Now that's a game I would like to see at the moment, our "Tuesday team" V our "Weekend team" :) 

Well, we often ended up beating ourselves last season....

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6 hours ago, RumRed said:

The way the draws have been handled in this shambolic cup, quite high.

I hear they're doing the draw in Compton Martin for the next round. At 2am. Outside the Ring O Bells. Hic.

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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:

Edited by Davefevs
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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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3 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.

Ooooooh, maths porn! :cool:

I reckon there are a few standard deviants on here!

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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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