A survey of 200 people yielded the following information: 94 people owned a Blu-ray player, 125 owned a microwave oven, and 72 owned both. How many people owned the following? (a) a Blu-ray player or a microwave oven (b) a Blu-ray player but not a microwave oven (c) a microwave oven but not a Blu-ray player (d) neither a Blu-ray player nor a microwave oven

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
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A survey of 200 people yielded the following information: 94 people owned a Blu-ray player, 125 owned a microwave oven, and 72 owned both. How many people owned the following?

(a) a Blu-ray player or a microwave oven
(b) a Blu-ray player but not a microwave oven
(c) a microwave oven but not a Blu-ray player
(d) neither a Blu-ray player nor a microwave oven
Expert Solution
Step 1

It is given that the total number of people surveyed is 200. So, the universal set U=200.

The number of people owned a Blu-ray player is n(B)=94.

The number of people owned a microwave oven is n(M)=125.

The number of people owned a Blu-ray player and a microwave oven is nBM=72.

(a)

Evaluate the number of people who own either a Blu-ray player or microwave oven as follows.

nBM=nB+nM-nBM=94+125-72=147

Therefore, the number of people who own either a Blu-ray player or microwave oven is 147.

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