Explanation Calculation: Case 1: The probability that they will all be in the same class Among 60 students, 30 students are assigned to first class and 30 students are assigned to second class. The total number of possible ways to select 30 students in first class is ( 60 30 ) . There are two possible ways to pick a class. Among the 5 second graders, all 5 students are assigned to first class. The number of possible ways to select all students in same class is ( 5 5 ) . The total number of remaining students is 55 ( = 60 − 5 ) and the number of students need to assign first class is 25 ( = 30 − 5 ) . After assigning five students to first class, the total number of possible ways is ( 55 25 ) . The probability that they will all be in the same class is, P ( all in same class ) = 2 ( 5 5 ) ( 55 25 ) ( 60 30 ) = ( 2 ) ( 1 ) ( 55 ! 25 ! ( 55 − 25 ) ) ( 60 ! 30 ! ( 60 − 30 ) ) = 2 ( 0.026 ) = 0.05 Thus, the probability that they will all be in the same class is 0.05. Case 2: The probability that exactly four of them will be in the same class Among the 5 second graders, 4 students are assigned to first class and the remaining one student assigned to second class. The number of possible way to select exactly four of them in the same class is ( 5 4 ) . The total number of remaining students is 55 ( = 60 − 5 ) and the number of students need to assign first class is 26 ( = 30 − 4 )

Mathematical Statistics and Data Analysis

3rd Edition

ISBN: 9781111793715

Author: John A. Rice

Publisher: Cengage Learning

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Chapter 1.8, Problem 30P

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Find the probability that they will all be in the same class.

Find the probability that exactly four of them will be in the same class.

Find the probability that Marcelle will be in one class and her friends in the other.

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Chapter 1 Solutions

Mathematical Statistics and Data Analysis

Ch. 1.8 - Prob. 1P Ch. 1.8 - Prob. 2P Ch. 1.8 - Prob. 3P Ch. 1.8 - Prob. 4P Ch. 1.8 - Prob. 5P Ch. 1.8 - Prob. 6P Ch. 1.8 - Prob. 7P Ch. 1.8 - Prob. 8P Ch. 1.8 - Prob. 9P Ch. 1.8 - Prob. 10P

Ch. 1.8 - Prob. 11P Ch. 1.8 - Prob. 12P Ch. 1.8 - Prob. 13P Ch. 1.8 - Prob. 14P Ch. 1.8 - Prob. 15P Ch. 1.8 - Prob. 16P Ch. 1.8 - Prob. 17P Ch. 1.8 - Prob. 18P Ch. 1.8 - Prob. 19P Ch. 1.8 - Prob. 20P Ch. 1.8 - Prob. 21P Ch. 1.8 - Prob. 22P Ch. 1.8 - Prob. 23P Ch. 1.8 - Prob. 24P Ch. 1.8 - Prob. 25P Ch. 1.8 - Prob. 26P Ch. 1.8 - Prob. 27P Ch. 1.8 - Prob. 28P Ch. 1.8 - Prob. 29P Ch. 1.8 - Prob. 30P Ch. 1.8 - Prob. 31P Ch. 1.8 - Prob. 32P Ch. 1.8 - Prob. 33P Ch. 1.8 - Prob. 34P Ch. 1.8 - Prob. 35P Ch. 1.8 - Prob. 36P Ch. 1.8 - Prob. 37P Ch. 1.8 - Prob. 38P Ch. 1.8 - Prob. 39P Ch. 1.8 - Prob. 40P Ch. 1.8 - Prob. 41P Ch. 1.8 - Prob. 42P Ch. 1.8 - Prob. 43P Ch. 1.8 - Prob. 44P Ch. 1.8 - Prob. 45P Ch. 1.8 - Prob. 46P Ch. 1.8 - Prob. 47P Ch. 1.8 - Prob. 48P Ch. 1.8 - Prob. 49P Ch. 1.8 - Prob. 50P Ch. 1.8 - Prob. 51P Ch. 1.8 - Prob. 52P Ch. 1.8 - Prob. 53P Ch. 1.8 - Prob. 54P Ch. 1.8 - Prob. 55P Ch. 1.8 - Prob. 56P Ch. 1.8 - Prob. 57P Ch. 1.8 - Prob. 59P Ch. 1.8 - Prob. 60P Ch. 1.8 - Prob. 61P Ch. 1.8 - Prob. 62P Ch. 1.8 - Prob. 63P Ch. 1.8 - Prob. 64P Ch. 1.8 - Prob. 65P Ch. 1.8 - Prob. 66P Ch. 1.8 - Prob. 67P Ch. 1.8 - Prob. 68P Ch. 1.8 - Prob. 69P Ch. 1.8 - Prob. 70P Ch. 1.8 - Prob. 71P Ch. 1.8 - Prob. 72P Ch. 1.8 - Prob. 73P Ch. 1.8 - Prob. 74P Ch. 1.8 - Prob. 75P Ch. 1.8 - Prob. 77P Ch. 1.8 - Prob. 78P Ch. 1.8 - Prob. 79P Ch. 1.8 - Prob. 80P

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Find the probability that they will all be in the same class. Find the probability that exactly four of them will be in the same class. Find the probability that Marcelle will be in one class and her friends in the other.

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Find the probability that they will all be in the same class. Find the probability that exactly four of them will be in the same class. Find the probability that Marcelle will be in one class and her friends in the other.

Chapter 1 Solutions

Find the probability that they will all be in the same class.

Find the probability that exactly four of them will be in the same class.

Find the probability that Marcelle will be in one class and her friends in the other.