What percentage of the total number of microstates are in one of the three most likely macro states of 100 coins being tossed (49 heads and 51 tails, 50 heads and 50 tails, or 51 heads and 49 tails)? Select the correct answer \( 8.9 \% \) \( 5.0 \% \) \( 47 \% \) \( 1.0 \% \) \( 24 \% \)
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- A microstate is a specific outcome of a system. In the case of tossing 100 coins, each unique arrangement of heads and tails is a microstate. - A macrostate is defined by a specific number of heads and tails, regardless of the order in which they appear. Show more…
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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? (b) What percent of the total possibilities is this? (Consult Table 15.4.)
What percent of the time will you get something in the range from 60 heads and 40 tails through 40 heads and 60 tails when tossing 100 coins? The total number of microstates in that range is $1.22 \times 10^{30}$ . (Consult Table $15.4 . )$
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