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.

What are the odds of me pulling the same card 5 days in a row. An unspecified card in the first place? Still 1/20?

OMFG, have your learned nothing from this thread. Day 1, you can pick any card, so that's 20/20, or 1/1. Let's say you pick the 3 of Clubs.

Odds of picking the 3 of clubs for the next 4 days is 1/20 each day. So 1 x 20 x 20 x 20 x 20 = 1/160K. That's the odds of picking the same card 5 days in a row. The odds of picking a specified card 5 days in a row would by 20 times less likely, so 1/3.2m

Would thinking of babies help? The probability of having a boy of 1/2.

If you want a boy the first time, the chance of getting one is 1/2.
You get one.
If you want a boy the second time, the probability of getting one that time is still 1/2.

The probability of having two boys is 1/2 x 1/2 = 1/4.

@Fainne - I’m sure if you apologise to purple for being both insulting and wrong, then people will probably give up on the bandwagon...

Put it this way, I know what I want, but I haven't told the person drawing the cards what card I want. I know what card I want, but they don't.

Does that make sense?

Are the odds different for me than they are for the dealer?

I want the Ace of Diamonds. Twice.

Then the probability of that is 1/400.

That is not what you were asking earlier but I like the clarity in this one.

Only the Ace of Diamonds? Are you certain that the King of Diamonds twice won't count?

Are you asking what the chances are of drawing it twice before you start the contest, or the chances of drawing it again, halfway through the contest?

*If you want a boy the first time, the chance of getting one is 1/2.
You get one.
If you want a boy the second time, the probability of getting one that time is still 1/2.

The probability of having two boys is 1/2 x 1/2 = 1/4.*

So what I want, changes the probability?

Put it this way, I know what I want, but I haven't told the person drawing the cards what card I want. I know what card I want, but they don't.
The odds of you getting what you want depends on what you want.
Two matching cards, or the same particular card twice.

The odds for the dealer depend on what the dealer wants.

If you want the ace of diamonds, first pick is 1/20
If you don’t care what the card is, first pick is 1/1 (call this card X)

Second pick to pick in a row...

If you want AoD again it’s 1/20 x the 1/20 from the first pick. So 1/400

If you want card X again it’s 1/20 x the 1/1 from the first pick. So 1/20

Babies is a good one. OP, can you not see that if you want 2 girls, and your friend wants 2 of the same sex, doesn't care if they are boys or girls, she is more likely to get what she wants. Because when you both have a boy, you cannot get what you want anymore. But she still can.

You need girl/girl. She needs a baby (lets say it was a girl), and then a girl.

So what I want, changes the probability?

Yes, because it changes the outcome of the first part. If you care what card it is, you have a 1 in 20 chance.

If you don’t care, it’s a 20/20 or a 1/1 chance that any card will come out.

This then becomes the starting point for the second pick.

1/20 or 1.

So what I want, changes the probability?

It doesn’t change the probability of the outcome.

It changes the probability of getting what you want.

Some outcomes are more likely than others.

Example: if I want two boys, I only have a 1/4 chance of getting what I want.
If I want one of each sex, I have a 1/2 chance of getting what I want.

That doesn’t affect in the slightest whether the baby that is born is a boy or a girl.

So you're saying it's what I want that determines probability. Fascinating.

And this my dear friends is why I've never taken a job at a bookies.

This is just staggering. Trying to explain this to the OP is like nailing jelly to a wall.

So you're saying it's what I want that determines probability. Fascinating.

No... by limiting the options from 20 to 1 for the first pick changes the question.

So you all agree that if I want the Ace of Diamonds, I get the Ace of Diamonds, then the odds of getting the Ace of Diamonds a second time is not 1/20.
No! It is 1 in 20.

The odds of you drawing an ace of diamonds twice in a row is 1 in 400.

If you've already drawn the ace of diamonds once (which was a 1 in 20 chance at the time), the odds of you drawing it on the second draw remains 1 in 20.

So you're saying it's what I want that determines probability. Fascinating.

Well if you pick a card, and you don't care what it is, then the chances of you getting what you want (a card) are absolutely certain. If you actually want a specific card, then less so.

"I want to draw the same card 2 days running" - a 1 in 20 chance.

"I want to draw the ace of diamonds 2 days running" ' a 1 in 400 chance.

Why did I come back?

Oh I'd feel sorry for OP if she wasn't so fucking rude. If only she'd take the time to try and understand the explanations instead of narrow-mindedly assuming she's right. 😂

So what I want, changes the probability?

Yes, because it's the probability of what you want. Like, if I want it to rain tomorrow, the probability of that is maybe 50%. But if I want to win the lottery, the odds are rather more against me.

PurpleDaisies and many others have it right. I have an MA in Maths from Oxford if we're piling up the qualifications.

So what I want, changes the probability?

Well of course it does.

If I don’t care which card I get on day one, I just want a card, my odds are 20/20 (or 1/1)
If I want a specific card on day one, then my odds are 1/20

If the OP is genuinely still struggling with this, let's go back to the coin example, so you're flipping a coin each day instead of drawing a card.

The four possible combinations are

Heads, Heads
Heads, Tails
Tails, Heads,
Tails, Tails

If you want to get the same side of the coin two days running, then two of the four outcomes (Heads, Heads or Tails, Tails) satisfy the criteria. A 2 in 4 possiblity (which simplifies to 1 in 2).

If you want to get heads to days in a row, then only 1 in 4 of the possible outcomes satisfies the criteria. A 1 in 4 chance.

In the second scenario, if you already successfully got Heads on day 1, then there's a 1 in 2 chance you'll get it again. The coin still only has two sides, after all.

Come on guys, stop arguing with the Stupid because we know what Stupid does! :o

@Fainne
Your not actually wrong.
But it's the bit about this.
Any card will do.... You get 20 choices.
A certain card .......You get 1/20 chance.