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" 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.

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

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.

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
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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!?

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.

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!

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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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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