We throw a symmetrical coin \(n\) times. Suppose that heads came up \(m\) times. The number \(m/n\) is called the frequency of the fall of heads. The number \(m/n - 0.5\) is called the frequency deviation from the probability, and the number \(|m/n - 0.5|\) is called the absolute deviation. Note that the deviation and the absolute deviation are random variables. For example, if a coin was thrown 5 times and heads came up two times, the deviation is equal to \(2/5 - 0.5 = -0.1\), and the absolute deviation is 0.1.
The experiment consists of two parts: first the coin is thrown 10 times, and then – 100 times. In which of these cases is the mathematical expectation of the absolute deviation of the frequency of getting heads is greater than the probability?