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Of the 150 houses in a certain development, 60 percent have : Multiple-choice Questions — Select One Answer Choice

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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
any other explanation
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
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Thank you for your answers. I wonder something though. How do you reconcile what you found with the formula
P(AUBUC)=P(A)+P(B)+P(C) - P(A^B) - P(B^C) - P(A^C) + P(A^B^C)? where ^ means intersection.
Because if I did that, I would find:
P(AUBUC) = 150 - 5
P(A)=90 P(B)=75 P(C)=45
P(A^B^C)=5
So the sum P(A^B) + P(B^C) + P(A^C) = 90 + 75 + 45 + 6 - (150-5) = 71 which sounds clearly false...
I looked at the topic on overlapping sets and I don't get why this doesn't match the formula given there.
Many thanks for your help!
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
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fraise wrote:
Thank you for your answers. I wonder something though. How do you reconcile what you found with the formula
P(AUBUC)=P(A)+P(B)+P(C) - P(A^B) - P(B^C) - P(A^C) + P(A^B^C)? where ^ means intersection.
Because if I did that, I would find:
P(AUBUC) = 150 - 5
P(A)=90 P(B)=75 P(C)=45
P(A^B^C)=5
So the sum P(A^B) + P(B^C) + P(A^C) = 90 + 75 + 45 + 6 - (150-5) = 71 which sounds clearly false...
I looked at the topic on overlapping sets and I don't get why this doesn't match the formula given there.
Many thanks for your help!




A= house with an AC
B= house with a Sun porch
C= house with a pool

|A|=150(.6)=90
|B|=150(.4)=75
|C|=150*(.3)=45
|AUBUC|=150-5=145
|A,B,C|=5

145=|AUBUC|=|A|+|B|+|C|-|A,B|-|A,C|-|B,C|+|A,B,C|=90+75+45-|A,B|-|A,C|-|B,C|+5
|A,B|+|A,C|+|B,C|= 90+75+45+5-150= 215-145= 70
This is the number of house with 2 or more of the amenities. So we need to subtract those that have all three.

But the intersection of A,B, and C as shown in the Venn Diagram above is in each of the intersections of two events.
That is we have |A,B,C| in |A,B|, |A,B,C| in |A,C|, and |A,B,C| in |B,C|.

So we need to subtract it three times.
70-3(5)
=70-15
=55

Final Answer: D
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Of the 150 houses in a certain development, 60 percent have [#permalink]
chacinluis wrote:
fraise wrote:
Thank you for your answers. I wonder something though. How do you reconcile what you found with the formula
P(AUBUC)=P(A)+P(B)+P(C) - P(A^B) - P(B^C) - P(A^C) + P(A^B^C)? where ^ means intersection.
Because if I did that, I would find:
P(AUBUC) = 150 - 5
P(A)=90 P(B)=75 P(C)=45
P(A^B^C)=5
So the sum P(A^B) + P(B^C) + P(A^C) = 90 + 75 + 45 + 6 - (150-5) = 71 which sounds clearly false...
I looked at the topic on overlapping sets and I don't get why this doesn't match the formula given there.
Many thanks for your help!




A= house with an AC
B= house with a Sun porch
C= house with a pool

|A|=150(.6)=90
|B|=150(.4)=75
|C|=150*(.3)=45
|AUBUC|=150-5=145
|A,B,C|=5

145=|AUBUC|=|A|+|B|+|C|-|A,B|-|A,C|-|B,C|+|A,B,C|=90+75+45-|A,B|-|A,C|-|B,C|+5
|A,B|+|A,C|+|B,C|= 90+75+45+5-150= 215-145= 70
This is the number of house with 2 or more of the amenities. So we need to subtract those that have all three.

But the intersection of A,B, and C as shown in the Venn Diagram above is in each of the intersections of two events.
That is we have |A,B,C| in |A,B|, |A,B,C| in |A,C|, and |A,B,C| in |B,C|.

So we need to subtract it three times.
70-3(5)
=70-15
=55

Final Answer: D



Hi, I wonder why 70 is the number of house with 2 or more of the amenities, isn's it exactly the number of houses with 2 amenities (|A,B|+|A,C|+|B,C|= 70)? We've already subtracted 5 houses that have all 3 amenities.
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
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The \(5\) houses that were subtracted were those that have zero aminities.

LucaZh00 wrote:
Hi, I wonder why 70 is the number of house with 2 or more of the amenities, isn's it exactly the number of houses with 2 amenities (|A,B|+|A,C|+|B,C|= 70)? We've already subtracted 5 houses that have all 3 amenities.
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
Carcass wrote:
Total houses = number with air conditioning + number with sunporch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things

150 = 0.6(150) + 0.5(150) + 0.3(150) - D - 2(5) + 5

150 = 90 + 75 + 45 - D - 10 + 5

150 = 205 - D

D = 55

Why are you multiplying the number with all three things by 2??
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
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It is a formula for the three overlapping set
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Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
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