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male with brown hair

by lukaswelker » Thu Apr 17, 2014 9:11 am
Hey Guys

Here goes the question,

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

Why is it not c?

let me know if you know :)
Many thanks
Lukas
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by ajaysingh24 » Thu Apr 17, 2014 11:58 am
lukaswelker wrote:Hey Guys

Here goes the question,

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

Why is it not c?

let me know if you know :)
Many thanks
Lukas
Question can be solved by Bayes' Theorem
we need to find P(M/B) = male with brown hair
P(M/B) = P(B/M) * P(A)/P(B)

above two statement give value of P(A) and P(B) but not of P(B/M)
So answer should be (E)
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by GMATGuruNY » Fri Apr 18, 2014 4:09 am
lukaswelker wrote: 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
Statement 1: Students with brown hair = 1/2 * 60 = 30.
Statement 2: Male students = 1/3 * 60 = 20.

It's possible that all 20 male students have brown hair.
In this case, P(male with brown hair) = 20/60 = 1/3.
It's possible that only 10 of the 20 male students have brown hair.
In this case, P(male with brown hair) = 10/60 = 1/6.

Since the probability can be different values, the two statement combined are INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Apr 18, 2014 6:03 am
lukaswelker wrote: 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 can also use the Double Matrix Method to visually represent the information for this question. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
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:
Image

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:
Image

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

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

case b:
Image
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 = E

-------------------------------------------
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by [email protected] » Fri Apr 18, 2014 1:57 pm
Hi lukaswelker,

Sometimes a DS question can just be dealt with by TESTing Values, thinking logically and defining the possibilities.

Here, we're told that there are 60 students. We're essentially asked how many are males AND have brown hair?

When thinking about his prompt, my first thought is that there are males and females, some people have brown hair and some don't. That's a LOT of unknowns.

Fact 1: 1/2 the students have brown hair.

So, 30 students have brown hair and 30 don't. I don't know how many of those 30 with brown hair are males. It could be 0, 1, 2,....up to 30.
Fact 1 is INSUFFICIENT.

Fact 2: 1/3 of the students are males.

So, 20 students are males and 40 are females. I don't know how many of those 20 males have brown hair. It could be 0, 1, 2,....up to 20.
Fact 2 is INSUFFICIENT

Combined, we still have lots of possibilities. The answer could be anything from 0 to 20.
Combined, INSUFFICIENT.

Final Answer: E

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