I'd appreciate it if you could help me
If you keep tossing a coin, the odds of getting a flip and a face are half and half.
Now, here's the problem!
When you keep tossing a coin,
Which pattern is most likely to appear? Think about it before you continue reading.
The answer is the same for all probabilities.
Next question.
back, back, back, back, back, back, back, back, back, back, back, back, back, back, back, back, back Suppose that backs are found 10 times in a row, as in the following example. Which is more likely to appear next, "Heads" or "tails"?
The answer is that both "Heads" and "Tails" have the same probability.
The correct answer to these two questions is counterintuitive. Somehow, I get the feeling that because the coin is currently showing more heads than tails, it will eventually get a reverse and try to keep the average. But coins have no memory, so they don't remember how they have worked in the past. Even if the coin has been flipped 100 times in a row just before, the next coin you throw will have the same probability of coming up heads or tails.
Then the 50% chance is a lie! You may be tempted to say, "Well, then, the 50% probability is a lie!
But it is not a lie. For example, if a coin is tossed 10 times and it comes out back-to-back, the ratio of heads to tails is 9:1.
If, after tossing a coin 10,000 times, you toss a coin 10 times and get back-to-back, back-to-back, back-to-back, back-to-back, back-to-back, back-to-back, back-to-back, back-to-back, then the average of backs and fronts for the 10,000 tosses is about 5000 to 5000, so the ratio of heads to backs is 5009:5001.
The bias from the previous 10 tosses is no longer noticeable.
Thus, as the number of throws increases, the bias becomes less noticeable, and the ratio of heads to tails gets closer to 50%. This is what we mean by the probability approaching 50%.
If you keep tossing a coin for a long time, there will always come a time when the difference between the number of heads and tails becomes zero.
And in the same way, if you keep tossing the coin for a long time, even a situation where the heads come up 100,000 times more often than the tails will surely occur. (Here, "tossing the coin for a long time" may be many orders of magnitude more than 100 million, or a trillion, or whatever.)
When the difference between the number of times you get "heads" and "tails" reaches zero, you may stop throwing, saying, "After all, the difference will become zero someday! and stop throwing, you will get the desired result, but that is only because you stopped when you happened to get the desired situation.
Any number of situations with a difference will happen, and a situation without a difference is one of them! In short, the impression is greatly influenced by 'when' you stop.
-- In "Separate, Pack, and Paint: A Mathematical Thinking Method You Can Read and Learn"
If you stop throwing when the heads come up 100,000 times more than the tails, you may think, "What? Isn't there something wrong with this coin?" But this kind of thing usually happens.
