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# A realtor selling houses located in a gated community determines that

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Math Expert
Joined: 02 Sep 2009
Posts: 56301
A realtor selling houses located in a gated community determines that  [#permalink]

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23 Apr 2018, 01:19
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Difficulty:

85% (hard)

Question Stats:

40% (02:18) correct 60% (02:16) wrong based on 48 sessions

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A realtor selling houses located in a gated community determines that the probability that a model home will be sold is 0.5, the probability that the house next door to the model home will be sold is 0.4, and the probability that at least one of the two houses will be sold is 0.8. What is the probability that the house next door will be sold if the model home is sold first?

(A) 0.15
(B) 0.2
(C) 0.25
(D) 0.3
(E) 0.4

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Re: A realtor selling houses located in a gated community determines that  [#permalink]

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23 Apr 2018, 19:08
1

Solution

Given:
• Probability that model home will be sold = 0.5
• Probability that the house next door to the model home will be sold = 0.4
• Probability that at least one of the two houses will be sold = 0.8

To find:
• The probability that the house next door will be sold, if the model home is sold first

Approach and Working:
For any two events A and B, the probability that A will happen, given that B happens, is determined by the following:
P(A|B) = $$\frac{(P(A ꓵ B))}{(P(B))}$$
Here, event A = selling of the house next door to the model home
event B = selling of the model house
P(A|B) = probability of event A happening, given that event B is happening
P(A ꓵ B) = probability that both events A and B happening
Therefore, P(A) = 0.4, P(B) = 0.5, and P(A ∪ B) = 0.8
Now, P(A ∪ B) = P(A) + P(B) – P(A ꓵ B)
Or, 0.8 = 0.4 + 0.5 - P(A ꓵ B)
Or, P(A ꓵ B) = 0.1
Therefore, P(A|B) = 0.1/0.5 = 0.2
Hence, the correct answer is Option B.

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Re: A realtor selling houses located in a gated community determines that  [#permalink]

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05 May 2018, 08:55
Thank you for the answer, just a qq-What about 0.5*0.4 assuming these are independent events?EgmatQuantExpert
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Posts: 2943
Re: A realtor selling houses located in a gated community determines that  [#permalink]

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05 May 2018, 11:14
mayank3003 wrote:
Thank you for the answer, just a qq-What about 0.5*0.4 assuming these are independent events?EgmatQuantExpert

In this case the assumption that the events are independent is incorrect. Check the question statement - it says: "What is the probability that the house next door will be sold if the model home is sold first"

Hope it clarifies.
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27 Jun 2019, 00:41
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Re: A realtor selling houses located in a gated community determines that   [#permalink] 27 Jun 2019, 00:41
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