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# What is the probability that a student randomly selected

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

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28 Apr 2014, 14:47
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This one is pretty easy I think. Since there's no overlap with the given conditions, just go with E.

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09 May 2014, 20:37
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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?
S1:- One-half of the students have brown hair.
S2:- One-third of the students are males.

Any insights? I think it was tricky and I am still confused!

Last edited by Narenn on 10 May 2014, 00:37, edited 2 times in total.

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10 May 2014, 00:31
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rmohan1234 wrote:
What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?
S1:- One-half of the students have brown hair.
S2:- One-third of the students are males.

Any insights? I think it was tricky and I am still confused!

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DS_Question.png [ 18.52 KiB | Viewed 27249 times ]

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10 May 2014, 01:09
rmohan1234 wrote:
What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair?
S1:- One-half of the students have brown hair.
S2:- One-third of the students are males.

Any insights? I think it was tricky and I am still confused!

S1: says 30 students have brown hair and 30 do not have brown hair --> we cannot use it directly to get the probability
S2: says 20 students are males and 40 are females --> we cannot use this also directly to find the probability

Together: S1 and S2 we still cannot determine how many of the 20 males students have brown hair

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10 May 2014, 02:22
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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!

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

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02 Dec 2014, 19:35
unknown to solve this problem = total brown male = bm
asnwer: bm/60

1. bm+bw = 30 not sufficient
2. m = 20 not sufficient

1&2. bm <= 20 so not sufficient.

nocilis 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.

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

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19 Dec 2015, 05:39
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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.

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

GCDS nocilis What is the probability that a student (20151219).jpg [ 26.39 KiB | Viewed 17012 times ]

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

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22 Sep 2016, 13:21
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nocilis 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.

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

[Reveal] Spoiler:
E

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

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23 Feb 2017, 06:14
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

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

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26 Sep 2017, 10:41
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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Re: What is the probability that a student randomly selected   [#permalink] 26 Sep 2017, 10:41

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