Row 1 - A 2 3 4 5 6 7 8 9 10 J Q K

Row 2 - A 2 3 4 5 6 7 8 9 10 J Q K

Row 3 - A 2 3 4 5 6 7 8 9 10 J Q K

Row 4 - A 2 3 4 5 6 7 8 9 10 J Q K

A deck of 52 cards is dealt out entirely onto this grid, Ace to King, beginning with Row 1, without replacement.

>The odds of drawing/matching an Ace on the first card are 1/13.

>What are the odds of matching each successive card, without replacement, WITH THE CONDITION THAT no prior card has matched the space it was placed on the grid?

That is, what are the odds to match each card, 2, 3, 4, all the way to the 52nd card - which would have to be a King to match, where there have been no prior matches?

We came up with this solution

Draw 1 = 1/13

D2-D52 = 1/13*12/13^(D-1)

Can you confirm whether this is correct or not?

Thank you very much for your time!

Also, I assume you didn't mean to show two 8s in each row?

Quote:Match52A 52 space grid is laid out A-K four times:

Row 1 - A 2 3 4 5 6 7 8 8 10 J Q K

Row 2 - A 2 3 4 5 6 7 8 8 10 J Q K

Row 3 - A 2 3 4 5 6 7 8 8 10 J Q K

Row 4 - A 2 3 4 5 6 7 8 8 10 J Q K

A deck of 52 cards is dealt out entirely onto this grid, Ace to King, beginning with Row 1, without replacement.

>The odds of drawing/matching an Ace on the first card are 1/13.

>What are the odds of matching each successive card, without replacement, WITH THE CONDITION THAT no prior card has matched the space it was placed on the grid?

That is, what are the odds to match each card, 2, 3, 4, all the way to the 52nd card - which would have to be a King to match, where there have been no prior matches?

We came up with this solution

Draw 1 = 1/13

D2-D52 = 1/13*12/13^(D-1)

Can you confirm whether this is correct or not?

Thank you very much for your time!

This can't be correct since the next card drawn would have 4/51 which doesn't follow your solution.

The first card is not an ace, so there is a 4/52 chance it was a 2 and a 44/52 chance of anything besides A or 2.

The probability of matching the first 2 is 4/52*3/51 + 44/52*4/51

Quote:Match52

>What are the odds of matching each successive card, without replacement, WITH THE CONDITION THAT no prior card has matched the space it was placed on the grid?

That is, what are the odds to match each card, 2, 3, 4, all the way to the 52nd card - which would have to be a King to match, where there have been no prior matches?

Maybe I've had a stroke, but I couldn't seem to understand what you are asking. Do you mean "what are the chances of matching the nth card with the stipulation that none of the n-1 cards have matched their position?"

I agree that the odds of matching an ace on the first card is 1/13.

However the odds of D2, matching the 2nd card given that the first card was not an Ace? I think there are two scenarios:

- the first card was not an ace or two, and the 2nd card is a two. 44*4/(52*51) =176/2652

- the first and 2nd card are both twos c(4,2)/c(52,2) = 6/1326

So the total probability of D2 is the sum of the two terms above which is 188/2652 =.07089. Whereas your formula would yield 1/13 *12/13 = 12/169 = 0.071006.

The piece of information you have overlooked is that when the previous cards do not match their grid spaces there is some chance that they have depleted the number of cards that would match the nth grid space.

PRECISELY! So what are the odds of a 3 on 3? We need to provide for multiple possibilities

1) The Game Ended on Ace

2) The Game Ended on 2

3) There are 4 threes

4) There are 3 threes

5 There are 2 threes

How would you factor this one?

I believe once you determine the answer, it will match the formula posted!

**WITH THE CONDITION THAT no prior card has matched the space it was placed on the grid?

So your solution has to be multiplied by 1- the chance there was an Ace --that is what the formula provides