I have a quarter.
One side is heads; the other tails.
Assuming that each side weighs the same, there is a 1:2 chance that heads will appear once the quarter is flipped.
1:2 = 50%
Everytime I flip the quarter there is a 50% chance that heads will appear.
If I flip the quarter 1 time there is a 50% chance that heads will appear on that flip.
If I flip the quarter 1,000 times there is a 50% chance that heads will appear for every flip.
Therefore your chances of flipping a coin 1,000 times repeateldy and getting heads, repeatedly, are 50/50, or 1 out of 2.
Good odds, but something tells me that I really don’t have a 50/50 chance of doing so. However it seems that it should occur more frequently, I mean, where else can you get odds like that and loose every time?
You are correct, the odds are 50-50 that the coin will be heads whe you flip it.
The “probability” is that when you flip it 1000 times it will come up heads 500 times, but the chances are still 50-50 for each time you flip it. So, if you have flipped the quarter 999 times and have 500 heads and 499 tails, the chance of heads is still 50-50 on the next flip.
If you play long enough, the probability is that you will end up even, but there is a 50-50 chance you won’t.
What you’re missing is that there’s also a 50% chance of tails on every flip. I’m not going to go through this for 1000 flips, but let’s look at 2 flips, then generalize.
On the first flip, you could get heads or tails. Same for the second. This means there are 4 possible outcomes for 2 flips: heads/heads, heads/tails, tails/heads, and tails/tails. As you can see, that means that for 2 flips, there is 25% chance of getting 2 heads.
As you can imagine, the chance of getting all heads on a fair coin goes down a lot by the time you’ve flipped 1000 times.
Yep. It also depends on when you are making the statement. If you haven’t flipped any yet, your chances of getting 1000 heads in a row is 0.5[sup]1000[/sup], which my calculator gives up on.
OTOH, if you’ve already flipped 999 heads (or tails) in a row, you’ve got a 50/50 chance of getting 1000 in a row. After all, the odds of something happening, no matter how remote, is always 100% after its already happened.