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In a given finance lecture, 30% of the students are finance majors, an

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In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 25 Oct 2016, 09:32
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In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%

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In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 25 Oct 2016, 10:03
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Ratio of male to female to total= 6:4:10

Total non-finance students= 100-30=70

Since the gender distribution is same. i.e.: 6:4

Male:female of non- finance students = 42:28

Probability = 42/100= 42%

D


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Re: In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 25 Oct 2016, 11:12
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duahsolo wrote:
In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%


Let no of attendees be 100

Finance = 30 ; Non Finance = 70
Females = 40 ; Males = 60

Quote:
The gender distribution for finance majors and non-finance majors is the same.


Total Attendees = Finance Majors + Non Finance Majors

Since, Ratio of Male : Females ( For finance majors and non-finance majors ) is the same , ratio of Males : Females to the total population will also be same...

Quote:
what is the probability that the student is neither female nor a finance major?


= 60 ( Males ) * 70 ( Non Finance ) /100

= 42%

Hence, answer will be (D)

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Re: In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 01 Aug 2017, 01:14
Ratio of male to female for both finance and non finance majors are equal which is 6:4.
Now if 100 is total attendees then 100-30=70 are non finance students.
From the above ratio 6/10*70=42 are non female and non finance students.
So the probability given by 42/100=42%.
Option D.
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Re: In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 03 Oct 2017, 20:26
duahsolo wrote:
In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%

Does the colored portion talk about ratio?
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Re: In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 14 Mar 2018, 09:16
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duahsolo wrote:
In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%


This question can be solved using the Double Matrix method.

Note: This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- Major (Finance or Non-Finance)
- Gender (Female or Male)

Since we're dealing with percents all the way through to the answer choices, let's make things easy on ourselves and say that there are 100 students in the lecture.
So, here's the setup.
Image

30% of the students are finance majors
So, 30 students are finance majors and 70 are not.
Image

40% of the students are female
We get:
Image

The gender distribution for finance majors and non-finance majors is the same.
In other words, there's a 40/60 female/male split among the finance majors and among the non-finance majors.
We get:
Image

What is the probability that the student is neither female nor a finance major?
In other words, what is the probability that the student is a male non-finance major?
Once we simplify the boxes . . .
Image
. . . we see that 42 of the 100 students meet this criteria.
So, the probability = 42/100 = 42%

Answer: D




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Re: In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 16 Mar 2018, 04:26
I calculated it this way, quite fast: 1 - 4/10 - 3/10 + ((3/10)*(4/10)) = 1 - 0,4 - 0,3 + 0,12 = 0,42 --> D
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Re: In a given finance lecture, 30% of the students are finance majors, an  [#permalink]

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New post 17 Oct 2018, 14:57
duahsolo wrote:
In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%

VERY beautiful problem, in which the Venn diagram ("overlapping sets") solves the problem nicely.

Image

\(? = {\rm{None}}\,\,\,\,\left( {\,{\rm{in}}\,\,100\,} \right)\)

The wording in red is clearly presented below and also in the diagram!

\({{{\rm{finance}}\,{\rm{majors}}\,\,{\rm{and}}\,\,{\rm{female}}} \over {{\rm{finance}}\,{\rm{majors}}}} = {{{\rm{non - finance}}\,{\rm{majors}}\,\,{\rm{and}}\,\,{\rm{female}}} \over {{\rm{non - finance}}\,{\rm{majors}}}}\,\,\,\, \Rightarrow \,\,\,\,{x \over {30}} = {{40 - x} \over {70}}\)

\({x \over 3} = {{40 - x} \over 7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,7x = 120 - 3x\,\,\,\,\, \Rightarrow \,\,\,\,x = 12\)

\({\rm{finance}}\,{\rm{majors}}\,\,{\rm{or}}\,\,{\rm{female }}\,{\rm{ = }}\,\,30 + 40 - x\,\,\mathop = \limits^{x\, = \,12} \,\,\,58\,\,\,\,\,[\,{\rm{simplifier}}\,]\)

\(? = {\rm{Total}} - 58\,\,\mathop = \limits^{{\rm{Total}}\, = \,100} \,\,\,42\,\,\,\,\,\,\,\left( {42\% } \right)\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: In a given finance lecture, 30% of the students are finance majors, an   [#permalink] 17 Oct 2018, 14:57
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