Final answer:
To find the number of possible ways to roll a 6, we can calculate the number of macrostates and microstates for tossing 6 coins. There are 64 possible microstates and 6 macrostates with 5 heads and 1 tail. The probability of rolling 5 heads and 1 tail is 9.375%, and it is 3.33 times more likely to roll 3 heads and 3 tails than 5 heads and 1 tail.
Step-by-step explanation:
To find the number of possible ways to roll a 6, we need to determine the number of macrostates and microstates for tossing 6 coins. Each coin can either land on heads or tails, so there are 2 possibilities for each coin. Since there are 6 coins, there are 2^6 = 64 possible microstates.
To determine the number of macrostates, we need to consider the different combinations of heads and tails. For example, to get 5 heads and 1 tail, there are 6 choose 5 = 6 ways to arrange the heads and tails. Thus, there are 6 macrostates with 5 heads and 1 tail.
To find the probability of tossing 5 heads and 1 tail, we can divide the number of microstates for that macrostate by the total number of microstates. In this case, the probability is 6/64 = 0.09375 or 9.375%.
To find how much more likely it is to toss 3 heads and 3 tails compared to 5 heads and 1 tail, we can take the ratio of the number of microstates for each macrostate. In this case, there are 20 microstates for 3 heads and 3 tails and 6 microstates for 5 heads and 1 tail. Therefore, it is 20/6 = 3.33 times more likely to toss 3 heads and 3 tails than 5 heads and 1 tail.