Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Oct 2016, 10:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Probability questions need help.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Jul 2010
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 8

Probability questions need help. [#permalink]

### Show Tags

03 Jul 2010, 12:54
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

Hello to all Experts in Statistics/Probabilities

Please help me to solve the 2 probabilities questions below.

Q1. Three men are seeking for public office. Candidate A and B are given about the same chance of winning but Candidate C is given the chance twice as either A or B. What is the probability that A does not win? What is the probability of B?

Q2. In a certain children school, a teacher randomly selects 5 pre-schoolers from a class consisting of 10 boys and 5 girls. What is the probability of getting all 5 girls? 5 boys? Four boys and 1 girl?

It will be great if detailed explanation to the solution is provided. Many thanks in advance.
[Reveal] Spoiler: OA
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 442

Kudos [?]: 1924 [1] , given: 210

Re: Probability questions need help. [#permalink]

### Show Tags

03 Jul 2010, 14:22
1
This post received
KUDOS
For the first question:

Let us assume the following:

P(A) = x
P(B) = x
P(C) = 2x

Sum of probabilities = 1

4x=1

x= $$\frac{1}{4}$$

From there P(A) = P(B) =x= $$\frac{1}{4}$$

P(A not winning) = 1-P(A) = 1- $$\frac{1}{4}$$ = $$\frac{3}{4}$$

For the second question, I am not sure if the solution is right, but here's my take on it:

Total ways of picking 5 students = 15C5 = $$\frac{15!}{10!*5!}$$ = 3003

Number of ways of picking 5 girls = 5C5 = 1

So, probability of 5 girls = $$\frac{Number of ways of girls}{Total ways of picking}$$ = $$\frac{1}{3003}$$

Number of ways of picking 5 boys = 10C5 = $$\frac{10!}{5!*5!} = 252$$

Probability of 5 boys = $$\frac{Number of ways of girls}{Total ways of picking}$$ = $$\frac{252}{3003}$$

Number of ways of picking 4 boys and 1 girl = 10C4*5C1 = $$\frac{10!}{4!*6!}*\frac{5!}{4!*1!}= 1050$$

Probability = $$\frac{Number of ways of 4 boys and 1 girl}{Total ways of picking}$$ = $$\frac{1050}{3003}$$
Math Expert
Joined: 02 Sep 2009
Posts: 35274
Followers: 6636

Kudos [?]: 85545 [1] , given: 10237

Re: Probability questions need help. [#permalink]

### Show Tags

03 Jul 2010, 14:41
1
This post received
KUDOS
Expert's post
jovic1104 wrote:
Hello to all Experts in Statistics/Probabilities

Please help me to solve the 2 probabilities questions below.

Q1. Three men are seeking for public office. Candidate A and B are given about the same chance of winning but Candidate C is given the chance twice as either A or B. What is the probability that A does not win? What is the probability of B?

Q2. In a certain children school, a teacher randomly selects 5 pre-schoolers from a class consisting of 10 boys and 5 girls. What is the probability of getting all 5 girls? 5 boys? Four boys and 1 girl?

It will be great if detailed explanation to the solution is provided. Many thanks in advance.

Q1. Three men are seeking for public office. Candidate A and B are given about the same chance of winning but Candidate C is given the chance twice as either A or B. What is the probability that A does not win? What is the probability of B?

As there are only 3 candidates and assuming that either one of them must win, then their chances of winning must add up to 100%. So if chances of winning of A is $$x%$$, then chances of winning of B will also be $$x%$$ and of C $$2x%$$. Hence $$x+x+2x=100$$% --> $$x=25%=\frac{1}{4}$$.

So chances of B winning is $$x=\frac{1}{4}$$

Now, if chances of A winning is $$\frac{1}{4}$$, then chances of not winning will be $$1-\frac{1}{4}=\frac{3}{4}$$.

Q2. In a certain children school, a teacher randomly selects 5 pre-schoolers from a class consisting of 10 boys and 5 girls. What is the probability of getting all 5 girls? 5 boys? Four boys and 1 girl?

$$Probability=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}$$

A. $$\frac{C^5_5}{C^5_{15}}$$, where $$C^5_5$$ is the # of ways to choose 5 girls out of 5 and $$C^5_{15}$$ is the total # of ways to choose any 5 children out of total 15.

B. $$\frac{C^5_{10}}{C^5_{15}}$$, where $$C^5_{10}$$ is the # of ways to choose 5 boys out of 5 and $$C^5_{15}$$ is the total # of ways to choose any 5 children out of 15.

C. $$\frac{C^4_{10}*C^1_{5}}{C^5_{15}}$$, where $$C^4_{10}$$ is the # of ways to choose 4 boys out of 5, $$C^1_5$$ is the # of ways to choose 1 girls out of 5 and $$C^5_{15}$$ is the total # of ways to choose any 5 children out of 15.

Hope it helps.
_________________
Manager
Joined: 22 Oct 2009
Posts: 242
GMAT 1: 760 Q49 V44
GPA: 3.88
Followers: 6

Kudos [?]: 87 [1] , given: 1

Re: Probability questions need help. [#permalink]

### Show Tags

03 Jul 2010, 19:23
1
This post received
KUDOS
jovic1104 wrote:
Hello to all Experts in Statistics/Probabilities

Please help me to solve the 2 probabilities questions below.

Q1. Three men are seeking for public office. Candidate A and B are given about the same chance of winning but Candidate C is given the chance twice as either A or B. What is the probability that A does not win? What is the probability of B?

Q2. In a certain children school, a teacher randomly selects 5 pre-schoolers from a class consisting of 10 boys and 5 girls. What is the probability of getting all 5 girls? 5 boys? Four boys and 1 girl?

It will be great if detailed explanation to the solution is provided. Many thanks in advance.

Just to save some people some time --

Q2: the reduced answers are:

5 girls: $$\frac{1}{3003}$$
5 boys: $$\frac{12}{143}$$
4 boys, 1 girl: $$\frac{50}{143}$$
Intern
Joined: 03 Jul 2010
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: Probability questions need help. [#permalink]

### Show Tags

03 Jul 2010, 20:51
Thanks to all your reply. Your answer and explanation really makes sense. Kudos points to all of you.
Re: Probability questions need help.   [#permalink] 03 Jul 2010, 20:51
Similar topics Replies Last post
Similar
Topics:
PS question: need help 2 23 Oct 2010, 02:55
2 Help with an easy probability question 4 18 Mar 2010, 23:56
1 HELP PROBABILITY QUESTION!!!!! 6 16 Jan 2010, 02:42
Prep Question...Need help 4 04 Jan 2010, 17:40
5 Probability Question - Please help 8 30 Aug 2009, 01:09
Display posts from previous: Sort by

# Probability questions need help.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.