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probability

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by [email protected] » Sat Dec 27, 2008 10:54 am
In a marketing survey for products A, B, and C, 1,000 people were asked which of the products, if any, they use. The three circular regions in the diagram above represent the numbers of people who use products A, B, and C, according to the survey results. Of the people surveyed, a total of 400 use A, a total of 400 use B, and a total of 450 use C.

A & C=125
A & B=125
B & C= 100
A&B &C=75

What percent of the people surveyed use product A or product B or both, but not product C ?
(A) 12.5%
(B) 17.5%
(C) 30%
(D) 40%
(E) 60%

C
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Source: — Problem Solving |

Re: probability

by parallel_chase » Sat Dec 27, 2008 2:44 pm
We have to find 3 values

only A + only B + A&B both

only A = A - (A&C) - (A&B) - (A&B&C) = 400 - 125 - 125 - 75 = 75

only B = B - (B&C) - (A&B) - (A&B&C) = 400 - 100 - 125 - 75 = 100

A&B = 125


TOTAL surveyed = 1000

75 + 100 + 125 = 300

(300/1000)*100 = 30%

This is much easier to do with Venn Diagram as compared with formula.

Hope this helps.
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