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# Each of the 50 students participating in a workshop is either an under

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Intern
Joined: 19 Dec 2015
Posts: 28
Each of the 50 students participating in a workshop is either an under  [#permalink]

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03 May 2016, 07:04
5
28
00:00

Difficulty:

55% (hard)

Question Stats:

59% (00:38) correct 41% (00:46) wrong based on 786 sessions

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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 $$\frac{1}{2}$$?

1) Of the participants, 24 are female.

2) Of the participants, 18 are graduate students.
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Re: Each of the 50 students participating in a workshop is either an under  [#permalink]

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03 May 2016, 07:55
21
1
5
Number of students = 50

St1: Female = 24 --> Even if all female are graduates, female graduate students < 25 --> Suffiicient

St2: Graduate students = 18 --> Even if all graduate students are female, female graduate students < 25 --> Sufficient

##### General Discussion
Manager
Joined: 18 Feb 2015
Posts: 85
Each of the 50 students participating in a workshop is either an under  [#permalink]

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15 Aug 2016, 08:29
Hi all,

I tried to answer this question in the matrix form as attached. The answer I got is correct however, Im not sure if thats the right approach as the information from both statements isn't matching. I interpreted "Each of the 50 students is either an undergraduate or a graduate student" as by putting 0 in the relevant columns as shown. Where am I wrong?

Attachments

Screen Shot 2016-08-15 at 18.26.08.png [ 36.31 KiB | Viewed 11225 times ]

Manager
Joined: 15 Mar 2015
Posts: 111
Each of the 50 students participating in a workshop is either an under  [#permalink]

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15 Aug 2016, 08:47
HarveyKlaus wrote:
Hi all,

I tried to answer this question in the matrix form as attached. The answer I got is correct however, Im not sure if thats the right approach as the information from both statements isn't matching. I interpreted "Each of the 50 students is either an undergraduate or a graduate student" as by putting 0 in the relevant columns as shown. Where am I wrong?

Youve written that 0 males are undergrads and 0 females are graduates.

You should have put the total in the margin.

Posted from my mobile device

The 'is either a or b' means theres no overlapping.
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Manager
Joined: 26 Jan 2015
Posts: 77
Re: Each of the 50 students participating in a workshop is either an under  [#permalink]

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15 Nov 2016, 03:25
Vyshak wrote:
Number of students = 50

St1: Female = 24 --> Even if all female are graduates, female graduate students < 25 --> Suffiicient

St2: Graduate students = 18 --> Even if all graduate students are female, female graduate students < 25 --> Sufficient

Beautiful explanation Vyshak!
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Intern
Joined: 23 Aug 2017
Posts: 2
Each of the 50 students participating in a workshop is either an under  [#permalink]

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29 Sep 2017, 11:13
How do we know it's not all the undergraduates that are female making F=32 hence p(f)=1/2? Why are we assuming from the info given on (2) that F=18 or less?
Manager
Joined: 23 Jun 2016
Posts: 98
Re: Each of the 50 students participating in a workshop is either an under  [#permalink]

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12 Nov 2017, 18:23
1
If P is the probability that a randomly selected participant will be a female graduate student, is P less than 1212?

I misread the statement as asking for P within "graduate student" subset only. That is, the probability < 1/2 of picking a female within graduate student. Did not realize that probability asked is for the entire set of 50 students...

Did anyone else ran into this silly error? Or could the problem be worded more carefully??
Manager
Joined: 18 Dec 2018
Posts: 51
Re: Each of the 50 students participating in a workshop is either an under  [#permalink]

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18 Dec 2018, 21:13
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.
Manager
Joined: 12 Jan 2019
Posts: 51
Re: Each of the 50 students participating in a workshop is either an under  [#permalink]

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12 Jan 2019, 21:24
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.
Re: Each of the 50 students participating in a workshop is either an under &nbs [#permalink] 12 Jan 2019, 21:24
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