Question

(a) If tossing 100 coins, how many ways (microstates) are there to get the three most likely macrostates of 49 heads and 51 tails, 50 heads and 50 tails, and 51 heads and 49 tails? 
(b) What percent of the total possibilities is this? 

Table 15.4 100-Coin Toss
Macrostate
Number of microstates
Heads Tails
(W)
100
99
1.0x10?
95
7.5x107
90
10
1.7×1013
75
2.4x 1023
25
60
40
1.4x 1028
55
6.1x 1028
45
51
9.9x 1028
49
50
1.0x 1029
50
49
9.9x 1028
51
45
55
6.1x1028
40
1.4x 1028
60
25
2.4x 1023
75
10
90
1.7×1013
95
7.5x107
99
1.0x102
100
Total: 1.27x1030
Expand
Transcribed Image Text

Table 15.4 100-Coin Toss Macrostate Number of microstates Heads Tails (W) 100 99 1.0x10? 95 7.5x107 90 10 1.7×1013 75 2.4x 1023 25 60 40 1.4x 1028 55 6.1x 1028 45 51 9.9x 1028 49 50 1.0x 1029 50 49 9.9x 1028 51 45 55 6.1x1028 40 1.4x 1028 60 25 2.4x 1023 75 10 90 1.7×1013 95 7.5x107 99 1.0x102 100 Total: 1.27x1030

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