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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # What is the probability that a student randomly selected  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Director Joined: 19 Nov 2004 Posts: 526 Location: SF Bay Area, USA What is the probability that a student randomly selected [#permalink] ### Show Tags Updated on: 08 Aug 2012, 03:37 4 30 00:00 Difficulty: 25% (medium) Question Stats: 69% (00:35) correct 31% (00:28) wrong based on 1279 sessions ### HideShow timer Statistics 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. Originally posted by nocilis on 02 Feb 2005, 21:38. Last edited by Bunuel on 08 Aug 2012, 03:37, edited 1 time in total. OA added. ##### Most Helpful Expert Reply MBA Section Director Affiliations: GMAT Club Joined: 21 Feb 2012 Posts: 5797 City: Pune Re: Probability [#permalink] ### Show Tags 09 May 2014, 23:31 11 6 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! Choice E is the answer. Attachment: DS_Question.png [ 18.52 KiB | Viewed 63776 times ] Please Note the following :- 1) Always post the question in relevant forum i.e. Problem Solving Question is PS forum, Data Sufficiency question is DS forum, GMATClub test Question in GC Test forum. 2) Always post the question along with OA 3) Search the forum before posting a new question. This question is already discussed here. _________________ ##### General Discussion VP Joined: 18 Nov 2004 Posts: 1378 ### Show Tags 03 Feb 2005, 08:53 1 1 "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. Manager Joined: 01 Feb 2005 Posts: 56 Location: NYC ### Show Tags 03 Feb 2005, 14:27 1 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? Intern Joined: 26 Dec 2005 Posts: 8 ### Show Tags 25 Apr 2006, 14:25 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 GMAT Club Legend Joined: 07 Jul 2004 Posts: 4854 Location: Singapore ### Show Tags 26 Apr 2006, 18:21 1 1 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 Senior Manager Joined: 15 Aug 2007 Posts: 251 Schools: Chicago Booth Re: Male with brown Hair-probability [#permalink] ### Show Tags 21 Mar 2008, 18:37 notahug wrote: Could you exlain further? 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. Manager Joined: 03 Jan 2008 Posts: 97 Re: Male with brown Hair-probability [#permalink] ### Show Tags 21 Mar 2008, 19:52 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 Senior Manager Joined: 21 Apr 2008 Posts: 443 Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon Re: math--probablity [#permalink] ### Show Tags 08 Oct 2008, 05:23 Hello, IMO: C I used the following matrix: Code: Brown Not brown Total Male Female Total 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 _________________ mates, please visit my profile and leave comments http://gmatclub.com/forum/johnlewis1980-s-profile-feedback-is-more-than-welcome-80538.html I'm not linked to GMAT questions anymore, so, if you need something, please PM me I'm already focused on my application package My experience in my second attempt http://gmatclub.com/forum/p544312#p544312 My experience in my third attempt http://gmatclub.com/forum/630-q-47-v-28-engineer-non-native-speaker-my-experience-78215.html#p588275 Math Expert Joined: 02 Sep 2009 Posts: 50580 Re: class of 60 [#permalink] ### Show Tags 29 Dec 2009, 10:15 6 4 kirankp 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 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. _________________ Intern Joined: 25 Apr 2010 Posts: 5 What is the probability that a student randomly selected [#permalink] ### Show Tags 30 Jul 2010, 21:56 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!? GMAT Tutor Joined: 24 Jun 2008 Posts: 1327 Re: Probability [#permalink] ### Show Tags 30 Jul 2010, 23:15 3 Samarth0711 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. 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. _________________ GMAT Tutor in Toronto If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Manager Joined: 14 Jul 2010 Posts: 68 Re: Probability [#permalink] ### Show Tags 01 Aug 2010, 22:10 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. Manager Joined: 24 Apr 2010 Posts: 56 Re: Probability [#permalink] ### Show Tags 09 Aug 2010, 01:37 1 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...) Intern Joined: 09 May 2014 Posts: 1 Re: Probability [#permalink] ### Show Tags 10 May 2014, 01:22 1 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! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6504 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the probability that a student randomly selected [#permalink] ### Show Tags 19 Dec 2015, 04:39 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. 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 53470 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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What is the probability that a student randomly selected  [#permalink]

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Updated on: 16 Apr 2018, 11:51
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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

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

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23 Feb 2017, 05:14
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, 09:41
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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