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

(1000 Posts)
Fainne Fri 24-Jan-20 00:23:47

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.

Are you replacing the card or not?

The odds are 1/20 that you will pull the card the first time. The odds are 1/20x20 that you will pull the same card the second time, and, each subsequent attempt, it increases by a factor of 20.

That is why lotteries are so profitable...

PurpleDaisies Fri 24-Jan-20 00:28:22

The probability of picking a specific card on two consecutive days is 1/400 as you said.

But that’s not the question... you said the SAME card so it could also be the ace of spades both days, or the ace of clubs etc.

There are 20 different cards available so instead of 1/400 it becomes 20/400 which is 1/20.

I hope that makes sense!

Fainne Fri 24-Jan-20 00:28:28

Yes - replacing the card.

You are correct that the odds of you getting the same card on both days are 1/400.

But I can see where the other person is coming from - because going into the second day, knowing that you want to get an Ace of Diamonds, the odds of you getting that card are 1/20.

PurpleDaisies Fri 24-Jan-20 00:29:07

I’ve assumed the card gets replaced. If not, there’s no possibility of getting the same card both days.

Bourdic Fri 24-Jan-20 00:29:14

Can’t sleep so I’ll have a go at this - my understanding is that as they are two completely independent events, you multiply.

Fainne Fri 24-Jan-20 00:29:50

Purple - I'm looking for the odds of me pulling the Ace of Diamonds out of a pack of 20 cards two days running.

Fainne Fri 24-Jan-20 00:32:00

I didn't want to get the ace of diamonds in the first place or the second place. But the odds of pulling the same card two days running is higher than the odds of simply pulling the card one day.

It's not cards I'm playing with/toying with.

Fainne Fri 24-Jan-20 00:32:47

Should read is lower exponentially........ Not higher!!!

PestyMachtubernahme Fri 24-Jan-20 00:33:40

The odds of getting the ace of diamonds on day one is 1/20.
The odds of getting the ace of diamonds on day two is 1/20.
The odds of getting the ace of diamonds on day one AND day two is 1/400.

Januarydontbecool Fri 24-Jan-20 00:37:45

@Fainne, the situations you mention at 00:23 and 00:29 are not the same.

Owlsintowels Fri 24-Jan-20 00:39:24

The probability of you getting the ace of diamonds two days running is 1/20 * 1/20 = 1/400

The odds of you getting the same card on the second day as whatever you pulled out on the first day is 1/20

So if you specify which card it is before you draw at all, odds are 1/400 of getting it twice. Ie 1/20 to get it once then 1/20 to get that same card again

If you don't care what you get the first time and just want it repeated then the odds are 1/20. Ie probability = 1 of getting a card the first time, then 1/20 of getting that same card the second draw

PurpleDaisies Fri 24-Jan-20 00:39:28

If you’re talking about a specific card on both days, it’s 1/400.

If you’re talking about matching cards, it’s 1/20.

I’ve written out a short version with the letters A-E. hopefully you can see there’s only one AA (probability 1/25) but five matching cards AA, BB, CC, DD, EE (probability 5/25 or 1/5).

If I have already drawn the Ace of Diamonds, replaced it, and shuffled, on day 1,

the odds I will draw any individual card, including the Ace of Diamonds is 1/20, because if you represent probability as a tree diagram, you've crossed off all the alternate outcomes that came off drawing any card other than the Ace of Diamonds. They can't happen, because they didn't

However, if you haven't drawn any cards yet, but you plan to draw twice, then the odds of drawing a named card, e.g. Ace of Diamonds, are 1/400.

The odds of just drawing any card twice are 20/400.

Januarydontbecool Fri 24-Jan-20 00:42:07

If I understand you correctly, at 00:23 it doesn’t matter what card you picked on Day 1. You’re just interested in the probability that you picked the same card on the second day.

On Day 2 there are 20 cards. One of those cards is the one you picked on Day 1, so the probability of picking that card again is 1/20.

Owlsintowels Fri 24-Jan-20 00:44:00

Fainne yes, the odds of pulling a specific card two days running are much lower than the odds of pulling that specific card just once

But the odds of getting two-in-a-row, of any old card, are the same as the odds of pulling a defined card.

So if you were running a promotion and giving a prize to people, you'd expect the same number of prizes given if you said "everyone who draws a queen of hearts wins" as if you said "everyone who pulls out the same card twice in a row wins"

It doesn't sound true, but it is!

PurpleDaisies Fri 24-Jan-20 00:47:00

It’s the same as the odds of two people having the same birthday as each other (assuming it’s equally likely that people will be born on any day of the year).

PurpleDaisies Fri 24-Jan-20 00:47:55

Sorry, missed the end off my post. It sounds like it should be less than 1/365 but it isnt.

Fainne Fri 24-Jan-20 00:54:05

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).

PurpleDaisies Fri 24-Jan-20 00:55:17

If it’s the same card on two consecutive days without specifying which of the twenty, the probability is 1/20.

Fainne Fri 24-Jan-20 00:55:50

But the odds of getting two-in-a-row, of any old card, are the same as the odds of pulling a defined card.

Do you not do Maths in England or something?

Fainne Fri 24-Jan-20 00:57:17

Purple - it doesn't matter whether I wanted it or not! Lol, the odds are still the same!!! Jeez. I'm having this same difficulty trying to explain this to the person I'm arguing with!

PurpleDaisies Fri 24-Jan-20 00:58:11

But the odds of getting two-in-a-row, of any old card, are the same as the odds of pulling a defined card.

I think you’ve misunderstood.

Look at my picture above.

For five cards A-E, the odds of getting an A from the deck is 1/5.
The odds of getting two of a kind of any card is also 1/5.
Those probabilities are the same.

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