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21 Sep 2019, 14:06
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D
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Difficulty:
65%
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Question Stats:
63% (02:03) correct
37%
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wrong
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The table above shows the number of residents in each of two age groups who support the use of each type of funding for a city initiative. What is the probability that a person randomly selected from among the 250 residents polled is younger than 40, or supports a type of funding that includes a tax, or both?
A. 1/5
B. 8/25
C. 12/25
D. 3/5
E. 4/5
PS43661.01
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21 Oct 2019, 06:43
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gmatt1476
Total Residents = 250
Let Younger than 40 condition be A and supports a type of funding that includes a tax condition be B
So we need to find \(\frac{P(A ∪ B)}{P(Total)}\) --- (1)
\(P(A ∪ B) = P(A) + P(B) - P(A ∩ B)\) --- (2)
Now,
P(A) = P(Younger than 40 condition) = 20 + 30 + 30 = 80 --- (3)
P(B) = P (supports a type of funding that includes a tax condition) = 20 + 30 +60 + 10 = 120 --- (4)
P(A ∩ B) = P (Both younger than 40 and Including Tax) = 20 + 30 --- (5)
Using (2), (3), (4), (5)
\(P(A ∪ B) = 80 + 120 - 50\)
\(P(A ∪ B) = 150\) --- (6)
Using (1) and (6),
\(\frac{P(A ∪ B)}{P(Total)}\) = \(\frac{150}{250}\) = \(\frac{3}{5}\)
Hence D
23 Mar 2021, 00:50
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giovannisumano
"both" means having both characteristics i.e. is less than 40 and supports tax.
We are given the number of residents who are "< 40" and "40 or more" and those who "support tax", "support fees" and "support both tax and fees". So the figures are very easy to work with.
e.g. how many residents less than 40 support only tax? 20
How many residents < 40 support both tax and fees? 30
etc
We need the number of residents who are either "<40" or "support includes tax".
We know that overall 20 + 30 + 30 = 80 residents are "< 40".
We know that of the residents "40 or more", 10 + 60 = 70 support taxes.
We need "a person that is younger than 40, or supports a type of funding that includes a tax, or both?"
80 people are < 40 and this includes those who are < 40 and support tax. So "both" is taken care of in this 80. Now we just add to it the number of people 40 or more who support tax i.e. 70.
Fav cases = 80 + 70 = 150
Total = 250
P = 150/250 = 3/5
Answer (D)
