Final answer:
In the context of coin tosses, entropy refers to the disorderliness of the macrostate. Moving from a 5 heads and 5 tails macrostate to a 2 heads and 8 tails macrostate represents an increase in entropy due to the transition to a less orderly state. The 5/5 configuration is statistically more likely than the 2/8 configuration because it has more microstates.
Step-by-step explanation:
The concept of entropy is closely associated with the level of disorder in a system. Looking at a situation involving a series of coin tosses can illustrate the change in entropy between different states.
Entropy and Coin Toss Macrostates:
Starting with 10 coins in a state of 5 heads and 5 tails and ending up with 2 heads and 8 tails, we have moved to a less orderly macrostate. This increase indicates a positive change in entropy. To quantify this change, we can look at the number of possible arrangements (microstates) that result in these macrostates. For the 5 heads and 5 tails state, there are significantly more ways to arrange the coins than for a state of 2 heads and 8 tails.
Comparing the likelihood of these states, the 5 heads and 5 tails configuration is more likely due to the higher number of microstates associated with it. If betting on 2 heads and 8 tails, accepting odds of 252 to 45 would not be favorable given that the 2 heads and 8 tails outcome has fewer microstates and hence is less likely than the more balanced outcome of 5 heads and 5 tails.