# 25 cards

1. Jun 11, 2007

### troloc

Good mornign folks. I have sought out this forum in hopes to end a continued arguement here in teh office. Below I will describe the situation. If you have time or interest in providing some directionit would be greatly appreciated.

25 card deck. 25 different cards. Shuffle then cut then show the top card. Do this twice. What is the probability of showing the same card twice?

It seems liek a simple 1/25 given that the card is defined and that it is merely 1 of 25. The question runs in two stages. A) the object card is unknown B) after teh first showing the object card is known and is only 1/25.

Thank you in advance folks and enjoy the day,

2. Jun 11, 2007

### NateTG

It is indeed a 1 in 25 chance that the two cards will be the same.

(This isn't a calculus question.)

3. Jun 11, 2007

### arildno

Probability to get a "workable" first card: 100%=1 (It doesn't matter what the first card; you can for any first choice reach the situation of also seeing it the second time)

Probability to get the right second card: 1/25

Thus, the total probability is 1*1/25=1/25

4. Jun 11, 2007

### troloc

Thank you for addressnig my post. I do apologize for posting in the wrong area.

So, if we allow the first card shown to be our object then the chance of a second showing are 1/25. This would be changed if we defined the card prior to the first showing, correct?

And again, thank you for the time you have spent.

5. Jun 11, 2007

### NateTG

If you know that the first card will be a 3, then it's still a 1/25 chance that the second card will be a 3.

6. Jun 11, 2007

### Figgs

Seems that you're saying:

Given that the first card is "X", what is the probability of drawing that card on the 2nd draw, which I agree is the same 1/25.

It seems to me the question itself is actually the probability of pulling the same card twice in a row, which would be multiplicative, right?

1/25 * 1/25, specifically the probability of pulling any given card (1/25) and then pulling that same card (1/25).

Figgs :)

7. Jun 11, 2007

### DeadWolfe

No. Why would the first probability be one in twenty-five. I cut and show the top card. Barring the deck exploding there is a one-hundred percent chance of this occurring.

8. Jun 11, 2007

### ssd

And the choice of the first card is in 25 ways. Therefore the answer is 25* (1/25)*(1/25) = 1/25.

9. Jun 11, 2007

### Figgs

I see the difference being:

What are the odds of pulling ANY card, twice in a row. (1/25)
versus
What are the odds of pulling THIS CARD (thus naming a card before the first pull) twice in a row. (1/25 * 1/25)

Figgs

10. Jun 11, 2007

### Werg22

I like to think about probability in terms of combinatorics. With two draws, there are 625 different possibilities, 25 of which have the same cards for the two draws. Hence a probability of 25/625 = 1/25.

11. Jun 12, 2007

### haiha

My way is : there are two actions in series. First is to take a card on top, this action is always successful and its probability is 1 of course. Second is the card on top must be the same to the one taken before, then its probability is 1/25.
Totally you multiply the two probabilities then create 1/25.

12. Jun 14, 2007

### picklefeet

I feel the most simplistic way to explain this would be by flipping a coin. What are the odds of flipping the coin and getting the same result twice in a row? 2:1 But the odds of getting a preselected result (let's say heads) twice in a row is 4:1 The odds of getting heads on the first flip is 2:1 the same odds apply to the second flip. 1/2 * 1/2 = 1/4 = 4:1

13. Jun 14, 2007

### Moo Of Doom

Picklefeet, I think you got your odds mixed up with probabilities. The odds for flipping a coin twice and getting the same result each time are even, that is, 1:1. The odds against getting heads both times are 3:1.

If the odds for event P are a:b, then the probability that P occurs is a/(a+b).

14. Jun 14, 2007

### picklefeet

Thanks for pointing that out Moo Of Doom,
Being as the original qeustion, what are the chances of pulling the same card from a deck twice in a row, probability would probably be the way to go. I just got phrases mixed up. I'm glad people are paying attention.

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