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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?

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

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.

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

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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient

Should be (E)

(1) Insufficient (2) Insufficient

(1) & (2) => 30 students have brown hair, while 20 students are male. No way of determining overlap. There can potentially be 20 male students with brown hair, or none at all. Insufficient.
_________________

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:

Code:

Brown Not brown Total Male Female Total 30 30

Adding 2 to the matrix above:

Code:

Brown Not brown Total Male 20 Female 40 Total 30 30

Let's define the unknows:

Code:

Brown Not brown Total Male x y 20 Female z w 40 Total 30 30

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
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I agree that statement 1) and 2) are both insufficient. That leaves us w/ either C or E. But if you multiply 1/2 * 1/3, doesn't that give you a probability for brown haired male (1/6)?

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.

E.

we don't the how many males have brown hair and how many females have brown hair.

I agree. Sentence one tells us nothing about the sex, Sentence two tells us nothing about the hair, so neither is sufficient on its own. Together, the info about males with brown hair and females with brown hair is still lacking. All we know is that the answer is between 0 and 1/3.

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.

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;

(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.

What is the probability that a student randomly selected [#permalink]

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30 Jul 2010, 22:56

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!?

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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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...)