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07 Aug 2026, 10:11
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A community center is organizing a weekend workshop. Each participant is assigned to exactly one of three groups: planning, reception, or materials. If one participant is selected at random from all the participants, is the probability that the selected participant is in the reception group greater than \(\frac{5}{8}\)?
(1) The probability that the selected participant is not in the materials group is less than 45%.
(2) The probability that the selected participant is not in the reception group is greater than 40%.
(1) The probability that the selected participant is not in the materials group is less than 45%.
(2) The probability that the selected participant is not in the reception group is greater than 40%.
07 Aug 2026, 10:11
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Official Solution:
A community center is organizing a weekend workshop. Each participant is assigned to exactly one of three groups: planning, reception, or materials. If one participant is selected at random from all the participants, is the probability that the selected participant is in the reception group greater than \(\frac{5}{8}\)?
We need to determine whether the probability that the selected participant is in the reception group is greater than \(\frac{5}{8}\). Since \(\frac{5}{8} = 62.5\%\), the question asks:
Is \(P(R) > 62.5\%\)?
(1) The probability that the selected participant is not in the materials group is less than \(45\%\).
This means the probability that the selected participant is in either the planning group or the reception group is less than \(45\%\). Therefore, the probability that the selected participant is in the reception group must also be less than \(45\%\):
\(P(R) < 45\%\)
So the answer to the question is NO.
Sufficient.
(2) The probability that the selected participant is not in the reception group is greater than \(40\%\).
This means the probability that the selected participant is in the reception group is less than \(60\%\):
\(P(R) < 60\%\)
So the answer to the question is NO.
Sufficient.
Answer: D
A community center is organizing a weekend workshop. Each participant is assigned to exactly one of three groups: planning, reception, or materials. If one participant is selected at random from all the participants, is the probability that the selected participant is in the reception group greater than \(\frac{5}{8}\)?
We need to determine whether the probability that the selected participant is in the reception group is greater than \(\frac{5}{8}\). Since \(\frac{5}{8} = 62.5\%\), the question asks:
Is \(P(R) > 62.5\%\)?
(1) The probability that the selected participant is not in the materials group is less than \(45\%\).
This means the probability that the selected participant is in either the planning group or the reception group is less than \(45\%\). Therefore, the probability that the selected participant is in the reception group must also be less than \(45\%\):
\(P(R) < 45\%\)
So the answer to the question is NO.
Sufficient.
(2) The probability that the selected participant is not in the reception group is greater than \(40\%\).
This means the probability that the selected participant is in the reception group is less than \(60\%\):
\(P(R) < 60\%\)
So the answer to the question is NO.
Sufficient.
Answer: D
