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.

[Fainne]

Purple - I'm not going to embarrass you.

I didn't ask for the separate odds of pulling the same card.

I asked for the odds of pulling the same card 2 days running.

[Fainne]

Did any of you pass Maths?

[PurpleDaisies]

I’m not embarrassed. I’m absolutely confident in my maths ability.

If you are asking about the possibility of pulling the same (unspecified in advance) card from a deck of twenty cards two days running that is 1/20.

Did you not bother to read my earlier post with diagram that explained why?

[Fainne]

Bless you purple. But no, you're wrong.

[PotholeParadise]

Question is what are the odds of having picked the same card on two consecutive days. (I don't think whether I wanted said card or not on either or both days comes into the mathematical probability).

We're not asking about your emotions, mate.

If on the dawn of day 1, (when t=0, if you will), I plan to draw a card, replace, reshuffle and redraw, my chance of getting the King of Spades is 1/20 * 1/20 = 1/400.

My chance of getting the Four of Hearts twice is, again, 1/400.

My chance of getting the Two of Clubs twice is, again, 1/400.

And so on.

As there are 20 cards, the cumulative chances that I will get the same card twice equals 20/400, which equals 1/20.

[Fainne]

Ok.

Let me try to make this simple.

We've got 20 cards. 1 of those is the Ace of Hearts.

I want to get the Ace of Hearts on Day one.

1/20 chance? With me so far?

Day 2.

What are the odds of me getting the Ace of Hearts again?

It's not 1/20. It's 1/400.

FFS.

[Lweji]

It's correct, though.

For a combination of 2 cards A: 1/(20x20)=1/400
Combination of 2 of any of 20 cards: 20x1/(20x20) = 20/400 = 1/20
Picking card A in day 1: 1/20

[PurpleDaisies]

Maybe all the letters confused you.

I’ll try again.

The probability of pulling an ace of spades followed by another ace of spades is 1/20 x 1/20 = 1/400

The probability of pulling an ace of clubs followed by another ace of clubs is 1/20 x 1/20 = 1/400

The probability of pulling an ace of diamonds followed by another ace of diamonds is 1/20 x 1/20 = 1/400

Etc etc etc

So since it doesn’t matter whether you need an ace of spades, clubs, hearts, etc etc etc you add up all the probabilities of those events occurring

1/400 + 1/400 + 1/400 .... twenty times in total because there are twenty different cards giving 20/400 which cancels down to 1/20.

[MabelTheCow]

It’s a question of at what point do you need them to be the same

If you use baby boys and girls instead (just because my brain reasons better with less options) your chance of having 2 boys is 1/2x1/2=1/4, your chance of having 2 girls is 1/4

HOWEVER

your chance of having 2 children with the same gender is 1/2 because your first child is 1/1 (because it doesn’t matter if it’s a boy or girl) and then x 1/2 once the gender has been set.

Does that help?

[PurpleDaisies]

I want to get the Ace of Hearts on Day one.

That is specifying which particular card you want to get two of. The probability of that is 1/400.

You said that you only wanted two if the same card, so on day one you could choose an ace of clubs, followed by an ace of clubs on day two. There are twenty different ways to get matching cards out of four hundred possible combinations of cards.

[Lweji]

The problem, OP, is that you have to define your problem correctly to start with.
You keep changing what the question is.

[PurpleDaisies]

Can you really not see the difference between

I need two ace of hearts.
I need two matching cards?

[PotholeParadise]

Fainne

If you ask after you've drawn the card the first time, it's 1/20, because multiplying outcomes is something you only do when they're independant outcomes.

It's happened, it's determined. We don't just multiply numbers for the hell of it, these represent all the possible things that can happen.

The 1/400 number comes from adding up all the possible combinations when you have (what equates to) two sets of identical cards. For example Three of Hearts followed by Six of Clubs is a possibility. All together there are 400 ways to mix them up.

But if you have already drawn and replaced card 1, there are only 20 more ways it can go.

[PurpleDaisies]

Ok, how about a question for you.

I have two dice that I roll at the same time.

1. What is the probability that they both show a six?
   
2. What is the probability that they will both show the same number?

[Fainne]

Ok. Really simple.

What are the odds of me picking the Ace of Spades out of a full deck of cards randomly - 2 days in a row.

Now. What are the odds of me picking the Ace of Spades out of a full deck of cards when I'm praying for the Ace of Spades - 2 days in a row.

Do you believe the odds change based on what I want? lol.

[PurpleDaisies]

What are the odds of me picking the Ace of Spades out of a full deck of cards randomly - 2 days in a row.

Now. What are the odds of me picking the Ace of Spades out of a full deck of cards when I'm praying for the Ace of Spades - 2 days in a row.

Do you believe the odds change based on what I want? lol.

No, in those situations the odds are 1/400 both times because you are specifically looking for one card to come out twice.

If you are only looking for two matching cards, the odds are 1/20.

[Fainne]

Finally we're getting somewhere Purple!

[PotholeParadise]

Do you believe in giving people enough respect to read their answers to the thread you made?
lol

[SmallChickBilly]

What is the person you're arguing with in real life saying?

[Fainne]

God almighty - I know most of you don't take Maths after GCSE but I didn't realise how bad the ability is!

Play poker with me any time.

[PurpleDaisies]

I am hitting my head against the wall here.

The issue is the difference between I want a specific card twice and I want the same card twice which you seem to have conveniently ignored.

[PotholeParadise]

Fainne, the problem isn't our maths, it's your English.

[PurpleDaisies]

I’m taking it as you’re trying to be unpleasant now because you can’t admit you were wrong.

[Fainne]

Purple. It doesn't matter if I prayed to the Sun to get the same card twice, or whether I didn't give a fuck which cards were pulled. The odds of pulling the same card twice remain the same lol. God almighty!

[PurpleDaisies]

I notice you didn’t answer my question about the dice yet.