Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781337026345
Author: Katz
Publisher: Cengage
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Chapter 22, Problem 55PQ
To determine
The probability of getting “snake eyes”.
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What is the probability that out of fh'e pcople, none have the same birthday?
You may assume that there are 365 days in a year for simplicity. [Hint: start
by working out the probability of two people not having the same birthday.]
a) Make a diagram showing how many distinct ways (how many microstates, the
multiplicity) there are of putting q = 2 indistinguishable objects in N = 3 boxes.
Assuming that all microstates are equally probable, what is the probability that
both objects are in the left-most box? What is the correct formula for the
mulitiplicity as a function of N and q?
b) Make a diagram showing how many distinct ways (the multiplicity) there are of
putting q = 2 distinguishable objects in N= 3 boxes. Assuming that all microstates
are equally probable, what is the probability that both objects are in the left-most
box? Label the two objects R and G. What is the correct formula for the
mulitiplicity as a function of N and q?
Below are the diagrams, started for you. Complete the diagrams.
distinguishable
indistinguishable
RG
•.
!R !G
Rather than insisting that all the molecules be in the left half of a container, suppose we only require that they be in the leftmost 99% (leaving the remaining 1% completely empty). What is the probability of finding such an arrangement if there are 100 molecules in the container? What if there are 10,000 molecules? What if there are 1023 ?
Chapter 22 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 22.2 - Prob. 22.1CECh. 22.4 - Prob. 22.2CECh. 22.5 - Prob. 22.3CECh. 22.7 - You have considerable intuition about whether some...Ch. 22.9 - Prob. 22.5CECh. 22 - Prob. 1PQCh. 22 - Heat Engines Figure P22.2 shows a Carnot cycle....Ch. 22 - Use a PV diagram such as the one in Figure 22.2...Ch. 22 - Prob. 4PQCh. 22 - Prob. 5PQ
Ch. 22 - Prob. 6PQCh. 22 - An engine with an efficiency of 0.36 can supply a...Ch. 22 - Prob. 8PQCh. 22 - Prob. 9PQCh. 22 - Prob. 10PQCh. 22 - Prob. 11PQCh. 22 - Prob. 12PQCh. 22 - Prob. 13PQCh. 22 - Prob. 14PQCh. 22 - Prob. 15PQCh. 22 - Prob. 16PQCh. 22 - Prob. 17PQCh. 22 - Prob. 18PQCh. 22 - Prob. 19PQCh. 22 - Prob. 20PQCh. 22 - Prob. 21PQCh. 22 - In 1816, Robert Stirling, a Scottish minister,...Ch. 22 - Prob. 23PQCh. 22 - Prob. 24PQCh. 22 - Prob. 25PQCh. 22 - Prob. 26PQCh. 22 - Prob. 27PQCh. 22 - Prob. 28PQCh. 22 - Prob. 29PQCh. 22 - Prob. 30PQCh. 22 - Prob. 31PQCh. 22 - Prob. 32PQCh. 22 - Prob. 33PQCh. 22 - Prob. 34PQCh. 22 - Prob. 35PQCh. 22 - Estimate the change in entropy of the Universe if...Ch. 22 - Prob. 37PQCh. 22 - Prob. 38PQCh. 22 - Prob. 39PQCh. 22 - Prob. 40PQCh. 22 - Prob. 41PQCh. 22 - Prob. 42PQCh. 22 - Prob. 43PQCh. 22 - Prob. 44PQCh. 22 - Prob. 45PQCh. 22 - Prob. 46PQCh. 22 - Prob. 47PQCh. 22 - Prob. 48PQCh. 22 - Prob. 49PQCh. 22 - Prob. 50PQCh. 22 - Prob. 51PQCh. 22 - Prob. 52PQCh. 22 - Prob. 53PQCh. 22 - Prob. 54PQCh. 22 - Prob. 55PQCh. 22 - Prob. 56PQCh. 22 - What is the entropy of a freshly shuffled deck of...Ch. 22 - Prob. 58PQCh. 22 - Prob. 59PQCh. 22 - Prob. 60PQCh. 22 - Prob. 61PQCh. 22 - Prob. 62PQCh. 22 - Prob. 63PQCh. 22 - Prob. 64PQCh. 22 - Prob. 65PQCh. 22 - Prob. 66PQCh. 22 - Prob. 67PQCh. 22 - Prob. 68PQCh. 22 - Prob. 69PQCh. 22 - Prob. 70PQCh. 22 - A system consisting of 10.0 g of water at a...Ch. 22 - Prob. 72PQCh. 22 - Figure P22.73 illustrates the cycle ABCA for a...Ch. 22 - Prob. 74PQCh. 22 - Prob. 75PQCh. 22 - Prob. 76PQCh. 22 - Prob. 77PQCh. 22 - Prob. 78PQCh. 22 - Prob. 79PQCh. 22 - Prob. 80PQCh. 22 - Prob. 81PQ
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- The grade appeal process at a university requires that a jury be structured by selecting four individuals randomly from a pool of thirteen students and six faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of two students and two faculty? (a) What is the probability of selecting a jury of all students? nothing (Round to five decimal places as needed.) (b) What is the probability of selecting a jury of all faculty? nothing (Round to five decimal places as needed.) (c) What is the probability of selecting a jury of two students and two faculty? nothing (Round to five decimal places as needed.)arrow_forwardSuppose we have four boxes. A, B, C and D containing coloured marbles as given below: Вох Marble colour Red White Black A 1 6 B 6 2 2 с 8 1 1 D 6 4 One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?arrow_forwardThree balls (labeled A, B, C) are placed into two different boxes (1 and 2), as in (Figure 1). If all arrangements are equally likely, what is the probability that all three will be in box 1?arrow_forward
- If 4 letters are put at random into 4 envelopes, what is the probability that at least one letter gets into the correct envelope?arrow_forward22. (2 points) What is the probability that exactly two customers arriving at the drive through lane in a fifteen minutes interval? (a) 0.2249 (b) 0.1378 (c) 0.2375 (d) 0.1237 23. (2 points) What is the probability that less than two customers arrive at the drive through lane in a fifteen minutes interval? (а) 0.2759 (b) 0.1991 (c) 0.1245 (d) 0.1874 24. (2 points) What is the probability that two or more customers arrive at the drive through lane in a fifteen minutes interval? (а) 0.8236 (b) 0.8009 (c) 0.7235 (d) 0.8921arrow_forwardSuppose there are 30 identical blue balls and 15 identical red balls in a bag. Without looking inside the bag, take a ball out of it and write down its color. Repeat this 10 times. What is the probability that 6 of these 10 balls are blue in each of the following situations? 1) What if we return the ball to the bag after each selection and then make the next selection? 2) What if we do not return the ball to the bag after each selection and then make the next selection?arrow_forward
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