
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 20th, 2017, 10:59 AM  #1 
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  Math question I can't figure out
So my teacher asked the class to figure out this question: A classroom with 24 students, containing: 8 girls and 16 boys, are going to a party together, in this party there's gonna be a princess and two princes selected at the end of the night by lottery. What would the chance be for 1 girl & 2 boys being selected? This might be simple for most of you, but please don't criticize me, I just struggle when it comes to probability, chances etc. I'd love an explanation & answer if possible. 
April 20th, 2017, 11:54 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,696 Thanks: 861 
we have to assume the selections are all independent of one another. Assume we chose 2 boys and then a girl Choosing the first boy has probability $\dfrac{16}{24}$ as there are 16 boys to choose from 24 students. Similarly the probability of choosing the second boy is $\dfrac{15}{23}$ as there are now 15 boys and 23 students to choose from. Finally the probability of choosing the girl is $\dfrac{8}{22}$ The total probability is the product of these since the selections are independent, so $p = \dfrac{16}{24}\dfrac{15}{23}\dfrac{8}{22} = \dfrac {70}{253}$ one can observe that this number remains unchanged if we change the order that the students were selected. For example if we chose the girl first we'd have $p = \dfrac{8}{24} \dfrac{16}{23}\dfrac{15}{22}$ and this is the same value as that calculated by assuming the selection was bbg. 
April 20th, 2017, 01:14 PM  #3  
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  Quote:
Last edited by emilo0212; April 20th, 2017 at 01:38 PM.  
April 20th, 2017, 02:04 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,696 Thanks: 861  Quote:
The correct answer is 40/253 apologies  
April 20th, 2017, 02:06 PM  #5 
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  

Tags 
figure, math, question 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Please help, I cannot figure this out, very short question.  Nmbvc0  Algebra  7  March 6th, 2013 08:49 AM 
Probability Question that I can't figure out  indiegod  Advanced Statistics  5  February 24th, 2010 08:07 AM 
Probability Question that I can't figure out  indiegod  Probability and Statistics  1  February 23rd, 2010 04:11 PM 
A Few Math Problems I Just Can't Figure Out  PugsMcGee  Applied Math  1  October 15th, 2008 08:54 AM 
Please Help, I cannot figure this out, very short question.  Nmbvc0  Calculus  0  December 31st, 1969 04:00 PM 