11. A real estate company is interested in determining how long a property stays
ID: 2921784 • Letter: 1
Question
11. A real estate company is interested in determining how long a property stays on the housing market before it gets sold. For a sample of 800 houses, they get the following table that summarizes the length of stay on the market and the house’s listed price.
Under 20 days
20-40 days
Over 40 days
Under $250,000
50
40
10
$250,000-$500,000
20
150
80
$500,000-$1,000,000
20
280
100
0ver $1,000,000
10
30
10
Based on this table, calculate the following probabilities:
(1) (2 points) What is the probability that a randomly selected house stays on the market for over 40 days?
(2) (2 points) What is the probability that a randomly selected house is listed under $250,000?
(3) (2 points) What is the probability that a randomly selected house stays on the market for over 40 days and is listed under $250,000?
(4) (2 points) For a house listed under $500,000, what is the probability that it gets sold under 40 days?
Under 20 days
20-40 days
Over 40 days
Under $250,000
50
40
10
$250,000-$500,000
20
150
80
$500,000-$1,000,000
20
280
100
0ver $1,000,000
10
30
10
Explanation / Answer
1) P(selected house stays on the market for over 40 days) = (10 + 80 + 100 + 10) / 800 = 0.25
2) P(selected house is listed under $250,000) = (50 + 40 + 10) / 800 = 0.125
3) P(elected house stays on the market for over 40 days and is listed under $250,000) = 10/800 = 0.0125
4) P(house gets sold under 40 days | house listed under $500,000) = P(house gets sold under 40 days and house listed under $500,000) / P(house listed under $500,000)
= [(50 + 40 + 20 + 150)/800] / [(50 + 40 + 10 + 20 + 150 + 80)/800]
= 260 / 350
= 0.7429
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