Consider a situation in which you have 10 coins on the table in a macrostate of
ID: 3163826 • Letter: C
Question
Consider a situation in which you have 10 coins on the table in a macrostate of 7H, 3T (7 show Heads, 3 show Tails). Say you randomly choose one of these coins to turn over (from T to H, or from H to T). a) What is the probability that you choose T (to be turned over to H), which would lead to a macrostate of 8H, 2T. (Calculate a value.) Explain. b) What is the probability that you choose H (to be turned over to T), which would Wad to a macrostate of 6H, 4T. (Calculate a value.) Explain. c) Therefore, if the current macrostate is 7H, 3T then what is the most probable macrostate after you choose a coin at random to flip over? And how many times more probable is this macrostate than the alternative? Explain. d) If the current macrostate is 8H, 2T then what is the most probable macrostate after the next coin (chosen at random) is flipped over? And how many times more probable is this macrostate than the alternative? Explain.Explanation / Answer
we have 10 coin 7 - H and 3 -T
theer are 3 chances for T and 7 chances for H
a) There are 3 Ts out of 10 the probabaility we choose T is 3/10 = 0.3 leads to micor state 8H,2T
b) There are 7 Hs out of 10, the probabaility that we choose H is 7/10 = 0.7 leads to 6H,4T
c) The most probable state after the turn from 7H,3T is 6H,3T as it ahs a probabaility of 0.7 compared to the other state which ahs a proabaility of 0.3 . It is 7/3 times moe probabale than the alternative
d) current state is 8H,2T
when T is flipped next state is 9H,T the probability is 2/10 = 0.2
when H is flipped next state is 7H,3T , the probability is 8/10 = 0.8
The most probable state is 7H,3T with probability 0.8 and it is 8/2 = 4 time more probabale than the other.