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? Select the correct answer \( 2.6 \times 10^{29} \) \( 5.1 \times 10^{29} \) \( 2.9 \times 10^{28} \) \( 3.0 \times 10^{29} \) \( 3.6 \times 10^{28} \)
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The problem asks for the number of ways (microstates) to achieve the three most likely outcomes (macrostates) when tossing 100 coins. These outcomes are 49 heads and 51 tails, 50 heads and 50 tails, and 51 heads and 49 tails. 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.)
Suppose you flip 50 fair coins. (a) How many possible outcomes (microstates) are there? (b) How many ways are there of getting exactly 25 heads and 25 tails? (c) What is the probability of getting exactly 25 heads and 25 tails? (d) What is the probability of getting exactly 30 heads and 20 tails? (e) What is the probability of getting exactly 40 heads and 10 tails? (f) What is the probability of getting 50 heads and no tails? (g) Plot a graph of the probability of getting $n$ heads, as a function of $n$.
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