Probability thread part II - what are the odds?

[Lweji]

www.mumsnet.com/Talk/am_i_being_unreasonable/3803785-to-ask-if-you-can-answer-a-question-re-probability-Maths-question?watched=1&msgid=93458537#93458537

You place the Bet before the event .
You have no knowledge of the result.

You have a knowledge of the chance of the result. If you don't have any knowledge of that chance then it's a different question.

Back to Monty Hall (sigh)... Rather than doors, imagine it with say 10 boxes. The way the problem is formulated is that you are being given the option between opening 1 box or opening 9. Obviously you're going to go for the 9 boxes every time, irrespective of whatever streak you are on. You would be stupid not to.

But say the 9 boxes are all placed one behind each other, so it only looks like one box. In that case, you have no knowledge of the chance, so it is a probability of 1/2. Or to put it in probability terms:
Chance of picking the 9 boxes and winning = 0.5 x 0.9 = 0.45
Chance of picking the 9 boxes and losing = 0.5 x 0.1 = 0.05
Chance of picking the 1 box and winning = 0.5 x 0.1 = 0.05
Chance of picking the 1 box and losing = 0.5 x 0.9 = 0.45

So, chance of winning = 0.45 + 0.05 = 0.5

But if you know which is the set of 9 boxes, your chance of winning = 0.9
Yes, it's not guaranteed to win, but you'd be pretty stupid not to go for the 9 boxes if you did know.

Checking in

mummmy2017 Mon 27-Jan-20 11:53:14
If your trying to win a second time in a row , you can't have lost the first time. If you can progress depends on the 1st result.

"In this case you're not betting before you know the results of the two tosses, then.
What?
Bet. See If you can toss heads twice in a row.
Not oh look you got a heads can you do it again."

I'm not betting on a chain after knowing the first result isn't positive.
I can bet on the second throw being the same as the first, with odds 1/2, because they are INDEPENDENT.

If you want to bet on a chain, you bet before the chain. You can walk home if the first result is not what you wanted. But the bet and the initial odds are still the same.

@chomalungma good to see you

The lottery is interesting. I think the idea of choosing numbers after 31 is good. It won't alter the chances of winning but will increase the potential sharing of a pot

Yes @chomalungma! I thought exactly the same

I don't think @mummmy2017 is coming back

Checking in ‘cause I can’t seem to stay away. 😬

Anyone come across the "boy born on a Tuesday" head bending?

I have two children. One of them is a boy born on a Tuesday. What is the probability that I have two boys?

@mummmy2017 go for it.

@BadLad - I was wondering if someone would bring that up! Those sort of questions were recently the topic of the Guardian puzzle set by Alex Bellos, and I fear there will be blood spilled here if we start arguing over it....

www.theguardian.com/science/2019/nov/18/can-you-solve-it-the-two-child-problem

Not sure I should, but checking in...

Crikey! You lot are persistent. I checked out of the last/first thread as it was doing my head in! And I was one that KNEW the bloody answer. The OPs utter intransigence and question changing totally befuddled me. I withdrew and hid it for my own safety

So, it goes like this. We choose families at random from the families with two children (excluding twins). This is in a world where boys and girls are equally likely, and can be born equally on any day of the week.

We are told that family A has at least one boy. Then the probability that both are boys is 33%. (1/3)

We are told that family B has at least one boy born on a Tuesday. Then the probability that both are boys is 48%. (13/27)

Seems weird that they are different, but it can be explained mathematically.

The lottery is interesting. I think the idea of choosing numbers after 31 is good. It won't alter the chances of winning but will increase the potential sharing of a pot

It will reduce the potential of sharing the pot, which is a good thing. Millions of people do birthdays, so going for numbers over 31 means you are less likely to have to share your win.

Also, buy your ticket just before the final deadline on the day of the draw. You are far more likely to die between buying the ticket and the draw, than you are to win. So buying the ticket as close to the draw as you can, reduces the chances of you buying a ticket and not living to see the draw.

Yeh, you can do that with a tree diagram. But it's one of those that even when you know the maths is correct it's really counterintuitive.

en.m.wikipedia.org/wiki/Boy_or_Girl_paradox

"Many people argued strongly for both sides with a great deal of confidence, sometimes showing disdain for those who took the opposing view."

I find this hard to believe...

I love probability and human psychology. I was watching a video last night on how to change people's mind. That was after a video on loss aversion

I am playing with this:

en.m.wikipedia.org/wiki/100_prisoners_problem

I don't think @mummmy2017 is coming back

I recognise the name - and behaviour - from the Brexit threads. They'll be back.

I've never come across the 2 Child problem before.
It has slightly blown my mind (statistics was never my strong point).

I've just fallen down the 2 child problem rabbit hole, too. I'd love to explain it to my dh, but I haven't grasped it firmly enough to do the necessary explanation. I can imagine tying myself up in knors.

Knots

It needs a diagram. A big diagram

I recognise the name - and behaviour - from the Brexit threads. They'll be back.

Ahhh!

I've just fallen down the 2 child problem rabbit hole, too

Me too. I understand the answer, mathematically. But it still ‘feels’ wrong. My mind can’t wrap itself around knowing how the day of birth can make any difference.

Please excuse that shocking grammar.