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A box contains 10 objects. Each object is either blue or red, and each object is either triangle-shaped or square-shaped. If an object is randomly selected from the box, is the probability greater than 0.8 that it’s blue, triangle-shaped, or both?
(1) P(red and square-shaped) = 0.2
(2) P(blue) = 0.8
(1) P(red and square-shaped) = 0.2
(2) P(blue) = 0.8
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06 Aug 2022, 03:26
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Considering the probabilities basis the information we get the below
R △ , B △ , R ▢ , B ▢
Overall R △ + B △ + B ▢ + R ▢ = 1
(1) P(red and square-shaped) = 0.2
R ▢ = 0.2
However, everything else has to sum up the requirement of the question (either △ or Blue or both)
=> R △ + B △ + B ▢ = 0.8
Since we get a definite answer that R △ + B △ + B ▢ is not more than 0.8, this is sufficient
(2) P(blue) = 0.8
Now we'll write the probability as
R △ + R ▢ + 0.8 = 1
But we don't know what is R ▢ as it could be 0 too. Hence, we cannot be whether that R △ + 0.8 > 0.8
Option A
R △ , B △ , R ▢ , B ▢
Overall R △ + B △ + B ▢ + R ▢ = 1
(1) P(red and square-shaped) = 0.2
R ▢ = 0.2
However, everything else has to sum up the requirement of the question (either △ or Blue or both)
=> R △ + B △ + B ▢ = 0.8
Since we get a definite answer that R △ + B △ + B ▢ is not more than 0.8, this is sufficient
(2) P(blue) = 0.8
Now we'll write the probability as
R △ + R ▢ + 0.8 = 1
But we don't know what is R ▢ as it could be 0 too. Hence, we cannot be whether that R △ + 0.8 > 0.8
Option A
08 Aug 2022, 07:56
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BrentGMATPrepNow
A box contains 10 objects. Each object is either blue or red, and each object is either triangle-shaped or square-shaped. If an object is randomly selected from the box, is the probability greater than 0.8 that it’s blue, triangle-shaped, or both?
(1) P(red and square-shaped) = 0.2
(2) P(blue) = 0.8
Given: A box contains 10 objects. Each object is either blue or red, and each object is either triangle-shaped or square-shaped. (1) P(red and square-shaped) = 0.2
(2) P(blue) = 0.8
One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of 10 objects, and the two characteristics are:
- blue or red
- triangle-shaped or square-shaped
So, we can set up our matrix as follows:
Target question: Is the probability greater than 0.8 that it’s blue, triangle-shaped, or both?
In the diagram below, the three shaded boxes represent objects that are blue, triangle-shaped, or both.
So, we can REPHRASE the target question as: "Is the sum of the three shaded boxes greater than 8?", since this would mean the probability is greater than 0.8 that the selected object is blue, triangle-shaped, or both.
Statement 1: P(red and square-shaped) = 0.2
When we add this information to our diagram we get:
This means the sum of the shaded boxes is 8.
So, the answer to the REPHRASED target question is NO, the some of the shaded boxes is NOT greater than 8
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: P(blue) = 0.8[/quote]
There are several scenarios that satisfy statement 2. Here are two:
Case a:
Here, the answer to the REPHRASED target question is NO, the some of the shaded boxes is NOT greater than 8
Case b:
Here, the answer to the REPHRASED target question is YES, the some of the shaded boxes is greater than 8
Since we can’t answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
To learn more about the Double Matrix Method, watch this video:
EXTRA PRACTICE QUESTION
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