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23 Apr 2018, 01:19
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:13) correct
43%
(02:06)
wrong
based on 160
sessions
History
Date
Time
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Not Attempted Yet
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
(A) 0.15
(B) 0.2
(C) 0.25
(D) 0.3
(E) 0.4
23 Apr 2018, 19:08
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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.
Answer: B
05 May 2018, 08:55
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Thank you for the answer, just a qq-What about 0.5*0.4 assuming these are independent events?EgmatQuantExpert
