Why is the probability largely different in this case? https://www.mathsisfun.com/data/binomial-distribution.html
In the given link, there is a problem regarding sandwiches (It comes under the red-colored heading, 'Bias', which comes after 3 such headings). It is concluded that 70% customers choose chicken yet we cannot anticipate that 7 out of next 10 will do so. (The probability of latter is just 27%.)
The math works out fine, with formulas of binomial distribution being made use of. But can anyone provide an intuition as to why this occurs ?
 A: The exact wording and the implications and meanings of the wording here are very important.
If I flip $10000$ coins, the expected number of coins that flipped as heads will be $5000$, that is to say in lay terms that if I repeat this experiment often enough and average the results, the average will be $5000$.
The chart showing the probabilities of getting various exact numbers of heads that we see in our $10000$ coin flips will start to look something like a bell curve.
We can even learn that the standard deviation of the number of heads will in this example be $\sqrt{10000\cdot 0.5\cdot 0.5}=50$.
Although getting $5000$ heads happens to be the most likely outcome when compared to the other possible outcomes, it is almost just as likely to have gotten $5001$ or $5002$ heads or so, each of which occurring only about $0.7\%\sim 0.8\%$ of the time a piece.  Actually looking at the probability of getting exactly $5000$ heads is not particularly meaningful.  Rather, we might prefer to talk about the probability of getting any number of heads between $4950$ and $5050$, any number of heads within one standard deviation of our average which would happen to occur about $68\%$ of the time.
The problem is made even worse if we are working with a range of possible values like on a real number line or similar... say for example if we were able to measure with exact precision the distance we throw a ball.  If we try and throw a ball and it bounces and we measure where exactly that occurred, suppose we throw the ball again and ask the probability that we hit the same exact location.  We might get very close to hitting the same space.. but even if we were so close that we couldn't tell the difference with our naked eye if we take a magnifying glass or a microscope we might find that were were off by a a few millimeters or even off by a few grains of sand or even smaller.
In fact, in several common probability scenarios, getting exact values might be so improbable that the only logical probability we can assign to that event is zero, something which occurs "almost never."  However, getting values within a particular range might be very probable.
It is almost impossible to find someone who is precisely $70.000004728100088927$ inches tall, but finding someone who is between $70$ inches tall and $71$ inches tall is relatively common.
