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Each of the 50 students participating in a

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Each of the 50 students participating in a

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Each of the 50 students participating in a workshop is either an undergraduate or a graduate student. If P is the probability that a randomly selected participant will be a female graduate student, is P less than 1/2?

1) Of the participants, 24 are female.

2) Of the participants, 18 are graduate students.

OA: D

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NandishSS wrote:
Each of the 50 students participating in a workshop is either an undergraduate or a graduate student. If P is the probability that a randomly selected participant will be a female graduate student, is P less than 1/2?

1) Of the participants, 24 are female.

2) Of the participants, 18 are graduate students.
Statement 1:
Since fewer than 1/2 of the students are female, the probability of picking a female graduate student must be less than 1/2.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
Since fewer than 1/2 of the students are graduate students, the probability of picking a female graduate student must be less than 1/2.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is D.

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Statement 1: Out of 50 students, only 24 are female.
This implies, that the probability that random student selected is a female is 0.48 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.
Statement 2: Out of 50 students, only 18 are graduate.
This implies that probability of total graduate is 0.36 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.

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Statement 1: Out of 50 students, only 24 are female.
This implies, that the probability that random student selected is a female is 0.48 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.
Statement 2: Out of 50 students, only 18 are graduate.
This implies that probability of total graduate is 0.36 i.e. less than 0.5
So, the probability that any selected candidate is a female graduate is surely less than 0.5. Hence, Sufficient.

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