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Suppose you flip 1000 coins.a) What is the probability of
Chapter 2, Problem 16P(choose chapter or problem)
Problem 16P
Suppose you flip 1000 coins.
a) What is the probability of getting exactly 500 heads and 500 tails? (Hint: First write down a formula for the total number of possible outcomes. Then, to determine the “multiplicity” of the 500-500 “macrostate,” use Stirling’s approximation. If you have a fancy calculator that makes Stirling’s approximation unnecessary, multiply all the numbers in this problem by 10, or 100, or 1000, until Stirling’s approximation becomes necessary.)
b) What is the probability of getting exactly 600 heads and 400 tails?
Questions & Answers
QUESTION:
Problem 16P
Suppose you flip 1000 coins.
a) What is the probability of getting exactly 500 heads and 500 tails? (Hint: First write down a formula for the total number of possible outcomes. Then, to determine the “multiplicity” of the 500-500 “macrostate,” use Stirling’s approximation. If you have a fancy calculator that makes Stirling’s approximation unnecessary, multiply all the numbers in this problem by 10, or 100, or 1000, until Stirling’s approximation becomes necessary.)
b) What is the probability of getting exactly 600 heads and 400 tails?
ANSWER:
Solution
Step 1
We know that probability describes the possibility of the outcomes of an experiment .
In this case the the number of ways to get 500 heads and 500 tails by flipping 1000
coins is given by
=
=
…………….(1)