100 coins are tossed randomly onto a table. The macrostate is defined as the number of heads that appear after the toss. A microstate is a specification of the outcome of each individual coin. What is the value for the number of heads that has the greatest number of possible microstates?
A) 95
B) 75
C) 60
D) 50

Question

Quizplus · Accepted Answer

The total number of possible microstates is 2^100, which is a very large number. The number of possible microstates for a given macrostate (i.e. the number of heads) is given by the binomial coefficient (100 choose X) where X is the number of heads. The graph of binomial coefficients peaks at the midpoint, which in this case is X=50. Therefore, the value for the number of heads that has the greatest number of possible microstates is 50.

100 Coins Are Tossed Randomly onto a Table