A question of probability - help please!

Some of yopu may be aware that we have been looking after our little grandaughter for about a year now as our daughter is seriously ill and in hospital. The dad has been off the scene for some time, until last September when he went to get court to get regular contact. Contact is on Sundays. He is a total ******, but that is not the point.

Over a period of 20 weeks he has missed contact with her 5 times. On those occasions, he says he has been ill. Fair enough.

However, it has now come to my notice that the local football team he plays for usually plays on a Saturday, But on 5 occasions they played on a Sunday, exactly the same 5 days that he says he "was ill".

The background to all this is actually quite interesting, if it wasn’t so serious, as he is now going for custody, but I need a little help from some of you with sharper, younger minds!

Now I studied statistics at A Level, but it was a long time ago. Now, for the life of me, I just cannot be sure how to do what should be a relatively simple probability calculation. My mind has gone blank!

The question is;

What is the mathematical probability of him “falling ill” on the exact 5 days that his football team just happened to playing on the Sunday, over a period of 22 weeks? And please show your workings as I will probably use this at the next court hearing!

 

Not sure you the need probability working out. It is blatantly obvious what has happened and maybe the team this bloke plays for could help or even the league they are in would probably have team sheets from the games. How is he going to work this if he gets custody? I loved maths at school but it was a long time ago and the memory is not what it was. If you had a bet on a single day off sick it would 365/1 but if you had it as an accumulator it would be 6567580836576/1 for for somebody to pick 5 days at random for somebody to be sick on over a year!
I'm sure some far greater minds will give a better answer than mine but I think it's fair to say that it's extremely unlikely to be sick on the same five days your team plays football!
I wish you luck and of course your daughter as well

 

I would have thought that courts would deal with facts rather then probability - I'd suggest getting a copy of his team's fixture list and mark it accordingly.

 

What a **** to prioritise playing football over seeing his kid.

 

Odds are going to be tiny aren’t they? 4 days average sick days per year divided by working days in year is percentage chance of being sick on one given day for an average worker. Seems reasonable assumption to start with. Exact 5 day combo would be that to power of 5?

 

Next time his team plays on a Sunday get a mate to go along and record it. That evidence along with anything else you can find which correlates his no shows with his team's past fixtures should be a slam dunk.

 

Thanks for the comments, and I agree wuith them but it was suggested by my barrister that I have the probablity as he will just say it is a coincidence.

I have a feeling that it is something like, as there are 140 days in the 20 weeks, and 5 games on Sundays......

5/140 x 4/139 x 3/138 x 2/137 x 1/136 as on his first day off sick he has 5 chances in 140, for the second he has 4 chances in 139, and so on.

Does that make sense?

If that is right, I'd like to show that in terms of 1 in y million, like the lottery odds.

 

I wouldn't worry about probabilities, stick to facts and let the judge work it out. Being sick one Sunday is just one of those things but missing 5 when his football team played, you need to find out if he played, if he did then he obviously lied. If possible get the court to find out from his employer whether he was off sick on the Monday after any of these missed days.

 

Mine is over 1 in a billion I think, using 4 days average sick days, 262 working days, so 1.5% to the power of 5. And that's over a year as well.

 

Don't you need a teamsheet in any level of football, handed in to the ref, recorded in perpetuity?

 

Thanks Jumbo, but he doesn't work!

 

Thanks everyone that has taken a look but I think I have the answer. The reference to the lottery made me think that, in effect, it would be similar to picking the right number out of 140, 5 times in a row, so I found this website.

http://www.easysurf.cc/lotodd.htm

I stuck in 140 in the first box, 5 in the next two boxes and it came out with

416,965,528 to 1.

Sounds good enough to me.

 

He's lying.
Best wishes to your daughter zz.

 

I think you are the closest but it is impossible to calculate unless you know his actual specific level of health.

If he is a particularly sick person then being ill on that number of Sundays is not that improbable.

Or he could be a heavy weekend drinker who has self inflicted "illness" on Sundays.

I think he is probably lying but proving he played football on those particular days, either through documentary or video evidence, is the only way to absolutely confirm that.

 

Hope you get it sorted.

Forgive me if I'm being a little too direct seeing as I don't know you, but your approach sounds like it could have turned into more of a personal vendetta & perhaps aimed at excluding the father further from his daughters life by claiming he was lying about being ill etc. You & your family would not have to deal with him so often, so whose purpose is this really for. (Rhetorical question).

There might be some unstated reason you object with the principle, why not slowly let him take more of the parental responsibility in his childs life, seeing as he's the father & his overall intent is to see the child more, even though his execution of that intent has been severely lacking on occasions. Perhaps look at the framing of it differently maybe along lines of he's far from perfect but at least its starting point with a potential better future on the horizon for all concerned? He will always be her father like that or not.

Like I say, hope it gets resolved.

 

I gave enough information to demonstrate the mathematical problem I wanted help with and I dont really want to go into it much more. But we are reluctant "parents" at our stage in life.

But I will say that there is such a potential for conflict in my and Mrs ZZ's thought processes that we specifically asked the court to appoint a Childrens Guardian, via CafCass, to look after the interests of our grandaughter in Court, rather than us who currently have equal parental rights with both my daughter and the father.

It's a horrible situation, and I wish it was over.

 

I don't think I explained myself properly last night.

The basic calculation would be:

A/B " A-1/B-1 * A-2/B-2 repeated until A = 0

Where A is number of days the person is sick in a period and B is the period in days.

For example, if someone is sick on 3 separate days over 3 weeks the calculation would be:

3/21 " 2/20 * 1/19

So choosing 3 specific days over a 3 week period is about a 1 in 10000 chance.

It doesn't matter whether you are estimating the chances of that being 3 Sundays, 3 Saturdays or a Wednesday, Friday and Monday. The probability is the same.

But illness doesn't work like that. It is far more likely that the days ill would be consecutive or near each other.

Some illnesses like migraines can occur randomly for just one day. But most occur over multiple days.

Injuries and drink related problems are more likely at weekends.

To get an accurate probability these need to be weighted in to any calculation.

But the thing you need to know the most is how many times was he ill during the 22 weeks other than the Sundays you know about.

Without knowing that it is impossible to calculate the probability of those illnesses occurring on specific days.

Bottom line is, that unless he is a very sick person, does activities on Saturdays that could lead to injuries or a heavy drinker on Saturdays, the chances of being sick 5 times on a Sunday in a 20 week period is very very remote.

 

Zztop from a fellow supporter, very sorry for you and you family you have the problem you have mentioned, very brave of you to share it with a group of people that you have probably never met! Many of us have grandchildren we are fortunate enough to " give back " when we have done our duties, unfortunately at this moment you are unable to do that, however let's hope things work themselves out and get easier for you!

Hopefully our good season and results so far have given you some good moments away from your problems!

 

Thanks, you are right, I ahve already gone down the route of looking on the teams website. But no luck.

What you say about all the parameters that could be taken into account is right, and so is what Sydney says along the same lines. But I was looking at it from a different, if simplistic, direction.

If the team was going to play on 5 days over the 20 weeks, and if someone was to be sick on 5 days over that 20 weeks, what is the probablity that they would fall on exactly the same days. That makes it a purely mathematical calculation, I believe.

 

Thanks Teide1, but to be honest I didn't start by planning to say so much abaout the situation. But thanks anyway!

 

Best wishes in your situation ZZ. My brother had similar issues with the deadbeat parents of their adopted child. I'm sure the courts will see through the BS.

Now just get your head right on brexit.

 

Yes, I got that. I see that I underestimated the chance of a game being played on Sunday. You are right, and that was my biggest mistake. Thereafter, I follow the rest.

I reckon that saying " less than 1 in a thousand", sounds good.

Thanks for your help, it is genuinely appreciated.

 

Sorry ZZ I didn't know about your daughter so my best wishes to you and your family. It must be a terrible situation. I'll PM you something about the football team.

 

Interesting methodology Nornironhorn. Where have you taken account of the fact that he has been sick 100% of the time when the match was on a Sunday ?

 

If you know what league they're in The FA full-time site might give you match reports/stats, generally as you get lower the amount of info reduces but it's worth a shot:
http://fulltime-league.thefa.com/Se...E212FBA?searchValue=ucl&submit.x=2&submit.y=8

 

Has the county FA affiliate got a website with the fixtures? Or can you write to the county FA and get the fixtures?

If his absenteeism can be correlated to the Sunday fixtures then you'd have a chance.

1 or 2 missed appointements maybe an anomaly however 5 is a pattern.

 

On the basis that it is binomial (he's either sick or he isn't) and we are picking a specific 5 days out of 20, why isn't it :-

(20 x 19 x 18 x 17 x 16) / (5 x 4 x 3 x 2 x 1) ?

 

Accepting that a person is sick 25% of Sundays just seems a wrong assumption. Surely that whole point is he isn’t really sick and is lying so you are trying to show the chances of an average person being sick on the exact days of his football matches (admittedly there is tons of missing information)?

 

Yeah not questioning the maths (you are more qualified than me) just seems a questionable first set of data (the claimed sick days by villain) to feed in initially.