1. ## Coincidence or not?

Is it a coincidence that:
The odds of picking an ace and then a heart WITHOUT REPLACEMENT is the same as picking the ace of hearts?

P(A,heart) = 1/52
P(1,heart)=P(Aheart,heart)+P(A notheart, heart)
= 1/52*12/51 + 3/52*13/51

= (12+39)/(52*51) = 1/52

Is this a coincidence or not, if so, prove it, if not, provide a counterargument.

2. The probability of picking the ace of hearts = $1/52$

The odds of picking an ace = $4/52 = 1/13$
the odds of picking a heart = $13/52$ = $1/4$

But if you first pick the ace of hearts, the odds of picking a heart afterwards becomes = $12/51$ = $4/17$

So if you first pick an ace not equal to the ace of hearts, the odds are $1/13*13/51=1/51$.

If you first pick the ace of hearts then the odds of picking a heart are $1/52*4/17=1/221$

This is what my beginner mathematical mind thinks... can be wrong...

Edit: Edited Mistakes

3. Originally Posted by xtheyinx
Is this a coincidence or not? If so, prove it.
What on Earth does that mean? How does one go about proving a coincidence? The entire distribution is easily specified. If you seek some mystical powers here, you are sure to be disappointed.

4. Originally Posted by TKHunny
What on Earth does that mean? How does one go about proving a coincidence? The entire distribution is easily specified. If you seek some mystical powers here, you are sure to be disappointed.
Well, I'm looking for some explanation that shows it is a coincidence lol.

5. Originally Posted by TKHunny
What on Earth does that mean? How does one go about proving a coincidence? The entire distribution is easily specified. If you seek some mystical powers here, you are sure to be disappointed.
Originally Posted by xtheyinx
Well, I'm looking for some explanation that shows it is a coincidence.
This thread should be moved to the forum on “Philosophy of Mathematics”.

6. Well I can tell you one thing... Math is an exact science, so it isn't a coincidence