Concept explainers
To construct: A table that represents the number of microstates corresponding to each macrostate.
To find: The probability of obtaining three heads and three tails. Also, probability of six heads.
Answer to Problem 47P
A table that represents the number of microstates corresponding to each macrostate is shown in Table 1. The probability of the three heads and three tails is
Explanation of Solution
Given:
Six coins are dropped on the floor after shaking.
Formula used:
A macrostate is defined as the overall property of a system, but it does not specify the details of the system like the order in which head or tails occurs. While microstate defines each sequence of the system, means a detailed description of every element of a system.
If n coins are tossed, then the total microstates will be
Probability for obtaining the given macrostate is,
Where,
Calculation:
Six coins are thrown. So, total number of microstates will be
There will be 7 macrostates for the given case.
The required table is shown below.
Table 1
S.NO | MACROSTATE | NUMBER OF MICROSTATES | |
1 | 6 HEADS | ||
2 | 5 HEADS, 1 TAIL | ||
3 | 4 HEADS, 2 TAILS | ||
4 | 3 HEADS, 3 TAILS | ||
5 | 2 HEADS, 4 TAILS | ||
6 | 1 HEAD, 5 TAILS | ||
7 | 6 TAILS |
The probability of obtaining 3 heads and 3 tails is,
The probability of obtaining 6 heads is,
Conclusion:
Therefore, the required table is shown in Table 1. Also, the probability of three heads and three tails is
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