to ask if you can answer a question re probability (Maths question)

[Fainne]

So, say I have 20 cards in a pack.

I pick one. It's the Ace of Diamonds let's say for argument's sake.

I then pick another one out of the same pack of 20 cards the following day.

Am I correct in saying that the odds of me picking the same card is a multiple of the single odds?

So 1/20 x 1/20 = 1/400

?

Because I've someone telling me the odds are still 1/20 that I'll pull the same card.

Yay! A maths thread!

Oh. A batshit maths thread.

So you're saying it's what I want that determines probability.
No. They are saying that if you change the question then you change the answer.
Haven't you grasped that yet?

What you want doesn't alter probability in some mystical way, but by specifying a particular card you have limited your options.
So if the card has to be ace of diamonds, only one of the 20 cards is the ace of diomonds, your chances are 1 in 20.
If all you want is a single card f t om that deck, doesn't matter which, your chances are 20/20 because whichever card you pick it will meet your criteria.
On day 2 if you want to match your random card, odds are 1 in 20 as only one of the 20 cards is the one you chose yesterday. Total odds 1 in 20.
If it had to be ace of diamonds on day 1 that is 1/20. If you pick it your chances on day 2 are also 1 in 20, you still have 20 cards, one is the ace. So, if you set a condition on day 1 it's 1/20 x 1 /20 =1/400

1. any card will do, as long as it matches

Day 1: 20/20
X
Day 2: 1/20
= 20/400 = 1/20

2. it must be ace of spades on both days

Day 1: 1/20
X
Day 2: 1/20
= 1/400

3. I have already drawn ace of spades on day 1 and it must match on day 2

Day 1: irrelevant
X
Day 2: 1/20
= 1/20

Surely someone's style of explanation must resonate with you OP? Or are you not bothering to try and understand?

OK so you have a card in mind but are keeping it secret. You draw this specific card on day 1 (still secret). The chances of drawing this specific card on day 2 is still 1/20.

Why is it not 1/400? Because you are ignoring the other 19 times out of 20 when you drew the 'wrong' card on the first day, as whatever you draw on the 2nd day will not bring about the desired outcome.

So the days where you drew the wrong card on day 1 are 19/20 days. All 20 draws on the second day will be wrong. So 19/20 * 20/20 = 19/20 (380/400)

The days where you draw the right card on the 1st day and the wrong card on the 2nd day are 1/20 * 19/20 = 19/400

The odds of failure, e.g. not drawing the right card each day is 380/400 + 19/400 (first day wrong + first day right & 2nd day wrong)
=399/400

Which leaves the chance of success at 1/400

(Maths degree and 2nd degree in Applied Accounting as we seem to need to post references)

NB I remember friends at university having a similar (and similarly frustrating) discussion about lottery numbers when the lottery first launched. Some people thought they should change their lottery numbers, if a specific number had come up the previous week. They were incorrect, as the chances of any number coming up each week is independent of what happened the week before.

Apart from 1 friend though, who acknowledged that statistically we were (probably) correct but superstitiously he liked to change his numbers when they had come up. That is fine. Using superstition to pick lottery numbers made full sense for him, as the chances of winning anything worthwhile are so low that you might as well get maximum enjoyment out of the process.

I don't think I've ever cringed so much as reading this thread. I'd feel sorry for the OP if they hadn't been so incredibly rude to basically the entire UK

Wow, this is a cringy thread. PurpleDaisies is spot on and explained very well.

I’m another fan of the Monty Hall puzzle and problems of that ilk. Here is one I like.
Note that strategy no.6 relates directly to the cards/dice problems explored in this thread.

A punter has one go on every Saturday’s lottery, picking the same numbers each week based on the day and month of the family’s birthdays. Would the following strategies increase, decrease or make no difference to the punter’s chance of winning the Jackpot.

1. Pick a better spread of numbers as birthdays do not include numbers over 31, and at least 3 of the punter’s numbers must be below 13.
2. Have a lucky dip instead.
3. Pick the numbers that have been drawn out the most over the previous two years.
4. Pick the numbers that have been drawn out the least over the previous two years.
5. Pick consecutive numbers. (eg. 11,12,13,14 etc.)
6. Pick the same numbers that were drawn last week.
7. Use a random number generator.

and for advanced students:

1. Do not enter for 51 weeks then have 52 lucky dips in one draw at the end of the year.

I'm abysmal at maths and even I get this, as does my 12 year old.

I agree with a PP, I'd feel bad for this poster if she hadn't been so unjustly and embarrassingly nasty.

This comment made me laugh so much for some reason -

The comments section on mysticbanana.com does not count as a credible source of mathematical information to me.

fucking hell its been while since I have seen such rude posts from an OP

these are all things you have said on this thread....

Do you not do Maths in England or something?
Jeez. I'm having this same difficulty trying to explain this to the person I'm arguing with!
Purple - I'm not going to embarrass you.
Did any of you pass Maths?
God almighty - I know most of you don't take Maths after GCSE but I didn't realise how bad the ability is!
PMSL. You guys really don't do maths do you?
Purple - could you and your sideways numbers, do one please?
Have I made your head hurt Spamantha?
Good Lord - you get worse with every post!
Is Maths just not taught over here or something?
To think that bar a few, most of you haven't a pig's arse clue of what you're talking about, is embarrassing for you.
How many dice will it take me to throw at you to make you go away?

and then you have the nerve to put this
Fainne Fri 24-Jan-20 15:16:59
Btw - there's absolutely no need for being so insulting to someone, even if you think they're thick as shit.

The odds of getting the same card twice in a row (if you don't care what card it is)=1/20
The odds of getting the ace of spades twice=(1/20)x(1/20)=1/400

This thread is quite something.

Odds of picking THE SAME card twice = 1/20
Odds of picking A PARTICULAR card twice = 1/400 (regardless of whether you “want” that card or not!)
Sorry for shouting..but OP is just not listening to reason!
Are you talking about picking a SPECIFIC card twice, or are you just picking A card twice? The answer obviously changes depending on the question..a point which are failing miserably to grasp and instead trying to blame on a lack of basic maths education in the UK 🤔
Nobody cares whether you personally want the card or not OP but it DOES matter whether you looking for a specific card to be pulled or not 🤷‍♀️

I know I'm just agreeing with everyone except the OP, but fwiw...

Kudos to PurpleDaisies for such patience and clear explanations. I'm not a natural mathematician like my DH but I find when the language used is clear and concise it's so much easier to grasp

A stats book I'd recommend to anyone who's interested is Reckoning With Risk, which is not by a statistician (I think!) but he shows how sometimes the statistics lead to quite counter intuitive results. There's an example on cancer screening that I found particularly interesting.

I'd also recommend any talk by David Spiegelhalter - there's a number on YouTube. I imagine his books are good too, but they're still on my "to read" list at the moment.

@PestyMachtubernahme puts it best

One of the many things the OP seems to be struggling with is she thinks that , on day 2 having already drawn the Ace of Diamonds once, there remains a 1 in 400 chance that the 2nd card drawn will be the Ace of Diamonds.

By similar logic, let's say the game was that you had to pull the Ace of Diamonds five days in a row. At the outset, the odds are 1 in 3,200,000.

The OP seems to think that, even if you had already successfully drawn the Ace of Diamonds 4 days in a row, that your odds of then drawing it on the 5th day remain 1 in 3,200,000, despite there only being one choice left to make with 20 cards to choose from.

Have not read the whole discussion but it might be useful to think about the entire probability space and what information people know for certain is true at the current time. Take the baby example. If you have 2 children, all the possibilities are: GG, GB, BG, BB.

IF you have not had any kids yet, the chance of you getting 2 girls is 1/4 (GG is 1 out of the 4 possibilities). The chance of you getting 2 of the same sex is 1/2 (GG or BB - 2 out of 4 possibilities).

Now, assume you have ALREADY had a Girl - this situation eliminates 2 of the possibilities (BB and BG) - it is impossible (if you only have 2 kids) for you to have either of those combinations. The only options open to you at this point are to have GG or GB. The chance of getting GG GIVEN that the first child is a girl, is 1 out of 2 (because GG is 1 out of the 2 options (GG or GB) available).

One of the many things the OP seems to be struggling with is she thinks that , on day 2 having already drawn the Ace of Diamonds once, there remains a 1 in 400 chance that the 2nd card drawn will be the Ace of Diamonds.

Excellent point.

Fainne

Imagine that you are in a hurdle race, with 400 other competitors.who are all equally good at running and jumping. At the beginning, the bookies say you have 1/400 chance of winning because there are 399 other people in the race with you.

Halfway through the race, you haven't fallen over yet, and 380 other people fell at the previous hurdle of the race. Your odds have irreversibly changed, because those other people are out and can't possibly win now.

At this point, you only have one more hurdle and 19 other people to beat. Your odds have improved to 1/20.

Btw - there's absolutely no need for being so insulting to someone, even if you think they're thick as shit.

@Fainne this is one of the most hypocritical comments I’ve read on MN. Have you gone back and read your posts from last night calling posters (and all English people!) thick? You were rude and patronising, and also wrong, so no wonder you’ve got a bit of a hard time on here today!

It's the 'and' vs 'or' in probability.

The chance of pulling that card out first time was 1/20. Second time though, it's a 1/20 of pulling the card out first time AND second time so it's 1/20*20 so 1/400 of getting the same card both times.

I think Fainne's silence now is telling us that the penny has finally dropped and she's realised that she was wrong and is obviously quite embarrassed about the way she was speaking to everyone as if she was surrounded by idiots.