Problem 1) a) What is the possible number of microstates associated with tossing a coin N times and having it come up H times heads and T times tails? b) For a series of 1000 tosses, what is the total number of microstates associated with 50% heads and 50% tails? c) How less probable is the outcome that the coin will land 40% heads and 60% tails? Solution Hi, N is number of units H is heads T is tails W is weight a) W = N! / (H! T!) b) you need to do some math here, I used a TI 83 calculator log (W) = log (1000!) 2 log (500!) = e 693 or exp (693) (it is a big number) c) log (W) = log (1000!) log (400!) log (600!) = e 673 or exp (673).

1. Problem 1)
a) What is the possible number of microstates associated with tossing a coin N times and having
it come up H times heads and T times tails?
b) For a series of 1000 tosses, what is the total number of microstates associated with 50% heads
and 50% tails?
c) How less probable is the outcome that the coin will land 40% heads and 60% tails?
Solution
Hi,
N is number of units
H is heads
T is tails
W is weight
a) W = N! / (H! T!)
b) you need to do some math here, I used a TI 83 calculator
log (W) = log (1000!) 2 log (500!) = e 693 or exp (693) (it is a big number)
c) log (W) = log (1000!) log (400!) log (600!) = e 673 or exp (673)