Answered: Let A,B,C⊆U. If n(U)=65, n(A)=24,…

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Let A,B,C⊆U. If n(U)=65, n(A)=24, n(B)=28, n(C)=32, n(A∩B)=15, n(A∩C)=7, n(B∩C)=11, and n(A′∩B′∩C′)=9, find n(A′∩B′∩C).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Let A,B,C⊆U. If n(U)=65, n(A)=24, n(B)=28, n(C)=32, n(A∩B)=15, n(A∩C)=7, n(B∩C)=11, and n(A′∩B′∩C′)=9, find n(A′∩B′∩C).

Expert Solution

Step 1

Given information:

$n (A^{'} \cap B' \cap C') = 9 n (U) - n (A \cap B \cap C) = 9 65 - n (A \cap B \cap C) = 9 n (A \cap B \cap C) = 65 - 9 = 56$

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