Choice E is the answer.

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"E" for me.....even after combining.....the 20 mals student might belong entirely to the gp of 30 brown hair students or may be 10, 5...etc....so insuff.

Vijo,
your answer cannot be right. We have 4 options of people:
P(A)=Male with brown hair
P(B)=Male with not brown hair
P(C)=Female with brown hair
P(D)=Female with not brown hair
By calculating P(A)=2/3, you are saying that P(B)+P(C)+P(D)=1/3 and that's when we have 2/3 female students and only 1/3 male students.
I believe we would need to know any of these four probabilities (P(A), P(B), P(C) , P(D) ) to answer the question, thus the answer is E?

E, as kook said there is no relationship

1) says nothing about males or females.

2) says nothing about hair color.

and

if 1 and 2 are taken together you could have all 30 brown hair as females and 0 brown hair males, or all brown hair males (20 of them) and 10 brown hair females. so NS

E

St1:
Insufficient. All we can gather is that 20 students have brown hair, and 40 students do not have brown hair.

St2:
Insufficient. All we can gather is that 20 students are male and 40 students are female.

Using both St1 and St2, we still cannot solve because we do not have breakdown of how many male students from the 20 males have brown hair.

Ans E

Probability is given by (no of male students with brown hair)/60

1 - Gives no information about students' gender. we just know that 30 students who have brown hair. Say this is n(B).
2 - Gives no information about students who have brown hair. we just know that 20 are male. Say this is n(M)

Combined - what we need is n(B∩M) = n(B) + n(M) - n(BUM). So we can't calculate n(B∩M) unless we know n(BUM) OR any other information that leads us to this information.

Hope this helps.

Thank you. Now I got it.

I remind that I once studied this:

p(MB)=probability of Male that is Brown hair
p(M)= probability of Male
p(B/M)= Probability of Brown hair person that is Male among group of brown hair people

What we need is p(MB), and p(MB)= p(M)*p(B/M) --> all we need is p(B/M) but both (1) and (2) give no information about it --> E

But I am not so sure its right.

Tks

Hello,

IMO: C

I used the following matrix:

Obviously, 1 and 2 alone are not suff. therefore, the point is if we can solve the problem with 1+2 (C or E)

With 1:



Adding 2 to the matrix above:



Let's define the unknows:



We can get the following eqs:

x+y=20
z+w=40
x+z=30
y+w=30

4 eqs and 4 unknows -> we can solve the problem

C

OA?

Cheers

We have four goups of students:
M(b) - Males with brown hairs;
M(n) - Males with non-brown hairs;
F(b) - Females with brown hairs;
F(n) - Females with non-brown hairs;

\(\frac{M(b)}{M(b)+M(n)+F(b)+F(n)}=\frac{M(b)}{60}=?\)

(1) \(\frac{M(b)+F(b)}{M(b)+M(n)+F(b)+F(n)}=\frac{1}{2}\) --> \(M(b)+F(b)=M(n)+F(n)\). --> \(\frac{M(b)}{M(b)+F(b)+M(b)+F(b)}=\frac{M(b)}{2M(b)+2F(b)}=\frac{M(b)}{60}\) --> Not sufficient.

(2) \(\frac{M(b)+M(n)}{M(b)+M(n)+F(b)+F(n)}=\frac{1}{3}\) --> \(2M(b)+2M(n)=F(b)+F(n)\) --> \(\frac{M(b)}{M(b)+M(n)+2M(b)+2M(n)}=\frac{M(b)}{3M(b)+3M(n)}=\frac{M(b)}{60}\). Not sufficient.

(1)+(2) Basically we have two equations with three variables. We can not express variables so that to get the numerical value of the fraction asked. Not sufficient.

Answer: E.
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What is the probability that a student randomly selected from a class of 60 students will
be a male who has brown hair?
(1) One-half of the students have brown hair.
(2) One-third of the students are males.

Is'nt this straightforward independant events probability:
(1/2)* (1/3) ??

That would get the answer as (C) but the correct answer is given as (E) ??
I know there's something really fundamental I am missing here!?

It's that they aren't 'independent events' - there's only one 'event' in the question, since we are only picking one student.

From the definition of probability, the probability of selecting a male with brown hair must be equal to:

(the number of males with brown hair) / (total number of students)

We know we have 60 students, so we just need to find the number of males with brown hair. This is really a Venn diagram question disguised as a probability question. We have 30 students with brown hair, and 20 males, but we don't know how these groups overlap. The people with brown hair might all be female, in which case we have 0 males with brown hair, or all 20 males could have brown hair, to take just the two extreme possibilities. So while we can find that the answer is somewhere between 0 and 1/3, we can't determine it exactly.
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I would draw a simple box here such as this one;

males | no males | total
brown | x | | (1)
no brown | | | (1)
total (2) (2) 60

x is asked here.
"One-half of the students have brown hair." will help us find (1)s. Not enough.
"One-third of the students are males." will help us find (2)s. Not enough

Using them together wont help us find x. Hence, E.

Spoiler of this question seems to be
well when we say 1/3 of 60 ie 20 are boys....it is actually not that all those 20 have brown hair....so we actually dont know actual numbers of boys who have brown hair....so E
(but i confess i was fooled at first glance...)

I think the answer should be (C). Please see the following approach and explain the flaw if possible:

I agree that "Male intersection Brown" can be anywhere between 0 and 20. Class is 60. This leads to probability being between 0 and 1/3.
But I disagree that we can NOT answer the question. The Answer should be 1/6. If we take the as mentioned by colleagues above, isn't the the entire concept of probability is lost?
Also, being male and brown hair are independent. When a person is born, BOTH of these traits are TOTALLY independent of each other.

Probability is a concept. Not a certainty, or a guarantee. It is only a likelihood.
Let me try and explain what I am saying.
Lets take a simple standard question for which there is no confusion.
# What is the Prob of getting all heads if I toss a coin 3 times.
Ans: We take sample space where we have 8 options. Favourable is 1. Answer is that probability is 1/8.

This means 1 out of 8 try's shall give us 1 success (3 Heads).

NOW

If I toss a coin 40 times can we say WE SHALL DEFINITELY GET 5 SUCCESSES ?

Obviously NO. But possible & likely.

If I toss a coin 40 times can we say WE SHALL DEFINITELY GET 0 SUCCESSES ?

Obviously NO. But possible.

If I toss a coin 40 times can we say WE SHALL DEFINITELY GET 40 SUCCESSES ?

Obviously NO. But possible.

So do we conclude that probability can be anywhere between 0 and 1.
As such, we do not have enough data to answer the question ? But, We say the probability is 1/8

I think we need to approach the Q39 in same way.

Any insights to refute/question my thinking process will be highly appreciated!

What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?

(1) One-half of the students have brown hair.
(2) One-third of the students are males.

In the original condition, the question is frequently given in the Gmat Math test, which is "2 by 2" que like the table below.

In the above, there are 4 variables((a,b,c,d), and 1 equation(a+b+c+d=60), which should match with the number equations. So you need 3 more equations. For 1) 1 equation, for 2) 1 equation, which is likely make E the answer.
When 1) & 2), you cannot find the value of b in a unique way from a+b=30, b+d=20, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Here's a step-by-step approach using the Double Matrix method.

Here, we have a population of students, and the two characteristics are:
- male or female
- has brown hair or doesn't have brown hair.

There are 60 students altogether, so we can set up our diagram as follows:


Target question: What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?
So, we must determine how many of the 60 students are males with brown hair. Let's place a STAR in the box that represents this information:


Statement 1: one-half of the students have brown hair.
So, 30 of the students have brown hair, which means the remaining 30 students do NOT have brown hair.
When we add this information to our diagram, we get:

Do we now have enough information to determine the number in the starred box? No.
So, statement 1 is NOT SUFFICIENT

Statement 2: one-third of the students are males
So, 20 of the students are males, which means the remaining 40 students are NOT males.
When we add this information to our diagram, we get:

Do we now have enough information to determine the number in the starred box? No.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Combining the information, we get:

Do we now have enough information to determine the number in the starred box? No. Consider these two conflicting cases:

case a:

Here, 0 of the 60 students are males with brown hair, so P(selected student is male with brown hair) = 0/60

case b:

Here, 5 of the 60 students are males with brown hair, so P(selected student is male with brown hair) = 5/60

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:

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Prompt analysis
The class have 60 student where they have brown haired and non brown haired student as well as male and female.
That means male(brown hair) + male (non brown hair) + female(brown hair) + female (non brown hair) =60

Superset
The answer will be in the range of 0-60

Translation
In order to find the answer, we need:
1# exact value of all the four parameter
2# atleast rest three parameters’ value

Statement analysis
St 1: male (brown hair) + female (brown hair) =30. Cannot say anything about male (brown hair). INSUFFICIENT
St 2: male (brown hair) +male (brown hair) = 20. Cannot say anything about male (brown hair). INSUFFICIENT

St 1 & St 2: three equation and four variables. Cannot derive the exact value. INSUFFICIENT

Option E

Why can't we treat this as probability? I fell for multiplying (1/2) and (1/3) and choose C. Can anyone explain why probability doesn't work in this situation?
(I was debating whether to use probability during the timed question. I even drew the table but was still perplexing).

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Hi,

How to identify whether a double matrix method can be used in a problem?

Thanks.
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