My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 23rd, 2013, 11:36 AM   #1
Newbie
 
Joined: Sep 2013

Posts: 4
Thanks: 0

University Stats - Simple Probability :)

Hi everyone, if someone can help me with this question/explain it it'd be helpful!

Consider a family with 3 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events "boy" and "girl" are independent.

a) what is the proability that all 3 children are male? notice that the complacement of the event "all three children are male" is "at least one of the children is female" use this information to compute the probabilty that at least one child is female

also- i thought the complacement meant the opposite of what they are trying to achieve, so wouldn't that be all 3 children are female?

THANKS!
robynfenty93 is offline  
 
September 23rd, 2013, 11:58 AM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: University Stats - Simple Probability :)

It is certain that either all three children are male OR at least 1 child is a girl...this is what makes the two events complements. To find the probability that all three children are boys, we need to consider the probability that the first child is a boy AND the second child is boy AND the third child is a boy, which gives us:



Now, because we know:



We may arrange this as:



And using our previous result, we find:



This is computationally simpler than using the binomial probability:



Whenever I see the words "at least one" in a probability problem, I take this as a cue to use the complements rule to greatly simplify matters, particularly when there are a large number of events. For three events, it's not too complicated to use the binomial formula, but for a larger number of events, it can be quite cumbersome, whereas the complement rule gets you there rather quickly.
MarkFL is offline  
September 23rd, 2013, 12:36 PM   #3
Newbie
 
Joined: Sep 2013

Posts: 4
Thanks: 0

Re: University Stats - Simple Probability :)

you are fantastic! thank you so much!
robynfenty93 is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
probability, simple, stats, university



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Stats Probability Help hamza101 Probability and Statistics 5 October 8th, 2012 08:46 PM
Need HELP with what is probably a simple stats question Completely Fed Up! Algebra 3 September 26th, 2012 05:42 PM
Stats/Probability help! jordanshaw3 Probability and Statistics 4 August 12th, 2011 08:14 PM
Need Help Please!!! Probability ans Stats agrabham Advanced Statistics 0 August 12th, 2008 11:08 AM
Need Help Please!!! Probability ans Stats agrabham Algebra 0 August 12th, 2008 11:06 AM





Copyright © 2019 My Math Forum. All rights reserved.