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Among a population of 30,000 people, 45 percent live within 10 miles Updated on: 03 Oct 2017, 11:17
Originally posted by Turkish on 03 Oct 2017, 11:12.
Last edited by Bunuel on 03 Oct 2017, 11:17, edited 1 time in total.
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81% (02:39) correct 19% (02:51) wrong based on 177 sessions

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Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20
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A
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Among a population of 30,000 people, 45 percent live within 10 miles 03 Oct 2017, 11:26
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Turkish
Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20
Show more

The number of people who live within 10 miles of their workplace but NOT inside the city limits of Town T = {Within 10 miles} - {Both} = 0.45*30,000 - 0.33*30,000 = 3,600

P = 3,600/30,000 = 3/25.

Answer: A.
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Among a population of 30,000 people, 45 percent live within 10 miles 03 Oct 2017, 22:25
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Turkish
Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20
Show more


We can solve this question just using the %, as all the values are given in % form.

45% live within 10 miles of their workplace
78% live inside the city limits of Town T
33% live both within 10 miles of their workplace and inside the city limits of Town T

the % person lives within 10 miles of their workplace but NOT inside the city limits of Town T= [% of People living in 10 mile radius of work place] -[% of People living in both winthin 10 mile radius and inside city limit]
=45% - 33% = 12%

Probability of % person lives within 10 miles of their workplace but NOT inside the city limits of Town T = 12/100 = 3/25 [12% out of 100%]

Answer: A
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Among a population of 30,000 people, 45 percent live within 10 miles 25 Oct 2017, 15:44
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Turkish
Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20
Show more

30,000 people
live within 10 miles: 30000(0.45) = 13,500
Live in city limits: 30000(0.78) = 23,400
Both: 30,000(0.33) = 9,900

People who live within 10 miles, but not in city limits 13,500 - 9,900 = 3,600

Probability of people who live within 10 miles, but not in city limits: 3,600/30,000 = 3/25

You do not need to really solve for the amount of people who live in city limits (78% of 30,000), I just did.
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Among a population of 30,000 people, 45 percent live within 10 miles 16 Feb 2026, 09:43
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Deconstructing the Question
Let A = lives within 10 miles of work.
Let B = lives inside city limits.
Given:
\(P(A)=45\%\)
\(P(B)=78\%\)
\(P(A\cap B)=33\%\)

We want A but not B.

Step-by-step

Only A:
\(P(A\text{ only})=P(A)-P(A\cap B)\)
\(=45\%-33\%=12\%\)

Convert to fraction:
\(\frac{12}{100}=\frac{3}{25}\)

Answer: 3/25
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