Question
In: Physics
a.) What is the change in entropy if you start with 50 coins in the heads...
a.) What is the change in entropy if you start with 50 coins in the heads macrostate, toss them, and get 24 heads and 26 tails?
b) What if you get 40 heads and 10 tails?
c) How much more likely is 24 heads and 26 tails than 40 heads and 10 tails?
d) Does either outcome violate the second law of thermodynamics?
e) In a few sentences, what does all of this coin tossing have to do with real physical systems?
Solutions
genius_generous answered 1 year agoRelated Solutions
A jar contains 100 coins. One of the coins is a trick coin with heads on...
A jar contains 100 coins. One of the coins is a trick coin
with heads on both sides. The other 99 coins are ordinary coins
with heads probability .5. A coin is selected at random. (a) What
is the probability the coin selected is the trick coin? (b) The
coin selected is tossed 7 times, and it happens to land heads each
of those times. Now what is the probability it is the trick
coin?
Problem 4) Five coins are flipped. The first four coins will land on heads with probability...
Problem 4) Five coins are flipped. The first four coins will
land on heads with probability 1/4. The fifth coin is a fair coin.
Assume that the results of the flips are independent. Let X be the
total number of heads that result.
(hint: Condition on the last flip).
a) Find P(X=2)
b) Determine E[X]
In tossing three fair coins, what is the probability of getting at least two heads?
In tossing three fair coins, what is the probability of getting
at least two heads?
Two coins are tossed. A die is thrown for each coin that falls heads. What is...
Two coins are tossed. A die is thrown for each coin that falls
heads. What is the expected number of spots shown on the dice?
Calculate the change in Entropy
A 288 kg block of ice at 0∘C is placed in a large lake the temperature of the lake is just slightly higher than 0∘C and the ice melts very slowly.
i) what is the entropy change of ice
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
Consider the following game. You are to toss three fair coins. If three heads or three...
Consider the following game. You are to toss three fair coins.
If three heads or three tails turn up, your friend pays you $20. If
either one or two heads turn up, you must pay your friend $5. What
are your expected winnings or losses per game?
You have 100 coins, and 99 of them are fair (equal probability of heads or tails)....
You have 100 coins, and 99 of them are fair (equal probability
of heads or tails). One of them is weighted and has a 90%
probability of landing on heads. You randomly choose one of the 100
coins. Find the probability that it is a weighted coin, under the
following scenarios: (Hint: if your calculator can’t compute 100!,
R can, just type factorial(100))
(a) You flip it 10 times and lands on heads 10 times (b) You
flip it 10...
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