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Each of the 30 students in a class is either male or female

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Each of the 30 students in a class is either male or female [#permalink]

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New post 30 Sep 2012, 00:03
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Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?

(1) The probability that the student will be both female and have brown hair is 0.1
(2) The probability that the student will be female minus the probability that the student will have brown hair is 0.25
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Sep 2012, 04:48, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Each of the 30 students in a class [#permalink]

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New post 30 Sep 2012, 04:35
Shawshank wrote:
Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?

1. The probability that the student will be both female and have brown hair is 0.1
2. The probability that the student will be female minus the probability that the student will have brown hair is 0.25


Two remarks:
a) Since the question is about a probability, we can consider 100 students or any other number, 30 is not important.
b) We can ignore that those who don't have brown hair can have either blonde or red hair.

We can work with Venn diagrams or the 2 X 2 table. And for either one, we can consider probabilities or actual number of people. For those who prefer visualizing.
Looking at the complementary probability, we see that in order to answer the question, it is enough to know the probability for MALE and NOT BROWN HAIR.
Or, if we know one of them, we must know the other one as well.

(1) Not sufficient.
We don't know how many male students with brown hair.

(2) Again not sufficient.
We don't know anything about the male students with brown hair.

(1) and (2) together: From the above, we can see that there is no information about the male students, and definitely there might be some of them with brown hair.
Not sufficient.

Answer E
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Re: Each of the 30 students in a class is either male or female [#permalink]

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New post 21 Jan 2014, 14:56
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Shawshank wrote:
Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?

(1) The probability that the student will be both female and have brown hair is 0.1
(2) The probability that the student will be female minus the probability that the student will have brown hair is 0.25


I suggest one just apply logic instead of Venn Diagram/Double set matrix

So what do we have here,
OK ...

We want P(F) + P(B) - (PuB) (We know they are not mutually exclusive as per the question stem

So we have

Statement 1

PuB = 0.1

Fair enough but I need more info

Statement 2

P(F) - (P(B)) = 0.25

We don't have enough info

Statements (1) and (2)

We need P(F) + P(B) - (PuB)
We have PuB = 0.1 and P(F) - (P(B)) = 0.25
Can I make it happen? Don't think so

E
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Re: Each of the 30 students in a class is either male or female [#permalink]

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New post 20 Oct 2015, 01:35
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Re: Each of the 30 students in a class is either male or female [#permalink]

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New post 21 Oct 2015, 03:17
Expert's post
Shawshank wrote:
Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?

(1) The probability that the student will be both female and have brown hair is 0.1
(2) The probability that the student will be female minus the probability that the student will have brown hair is 0.25


Given: Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair
Required: what is the probability that the randomly student will either be female or have brown hair
Let P(F) = Probability of Female
P(B) = Probability of Blonde hair

We need P(F) + P(B) - P(F) n P(B)

Statement 1:
P(F) n P(B) = 0.1 (i)
We do not know anything about P(F) + P(B)

INSUFFICIENT

Statement 2:
P(F) - P(B) = 0.25 (ii)
We cannot find P(F) + P(B) - P(F) n P(B)

INSUFFICIENT

Statement 1 and Statement 2 Combined :
Using (i) and (ii) also, we cannot find P(F) + P(B) - P(F) n P(B)

INSUFFICIENT
Option E
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Re: Each of the 30 students in a class is either male or female   [#permalink] 21 Oct 2015, 03:17
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