(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? (Consult this table.) ___________________ (b) What percent of the total possibilities is this? ____________________%

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(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? (Consult this table.)
___________________
 
(b)
What percent of the total possibilities is this?
 ____________________%
100-Coin Toss
Macrostate
Number of microstates
Heads
Tails
(W)
100
1
99
1.0x102
1
95
7.5x107
5
90
10
1.7×1013
75
2.4x1023
25
60
1.4x1028
40
55
6.1x1028
45
51
9.9x1028
49
50
1.0x1029
50
49
9.9x1028
51
45
55
6.1x1028
40
1.4x1028
60
25
2.4x1023
75
10
1.7×1013
90
95
7.5x107
99
1.0x102
100
Total: 1.27x1030
Transcribed Image Text:100-Coin Toss Macrostate Number of microstates Heads Tails (W) 100 1 99 1.0x102 1 95 7.5x107 5 90 10 1.7×1013 75 2.4x1023 25 60 1.4x1028 40 55 6.1x1028 45 51 9.9x1028 49 50 1.0x1029 50 49 9.9x1028 51 45 55 6.1x1028 40 1.4x1028 60 25 2.4x1023 75 10 1.7×1013 90 95 7.5x107 99 1.0x102 100 Total: 1.27x1030
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