
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 29th, 2017, 06:46 PM  #1 
Newbie Joined: Feb 2017 From: USA Posts: 7 Thanks: 0  Help with probability!
Hello, I am currently struggling to answer the following example: What is the minimum number of children (N) a couple should have in order to achieve both a male and female child with 99% probability? (Given the presumptions that the chances of having either a boy or girl is 50/50, and each sex at birth is independent of previous births) Any help would be great!! 
September 29th, 2017, 07:00 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,772 Thanks: 481 
Let's just do this with coin flips or bitstrings. The probability of a string of $n$ 0's is $\frac{1}{2^n}$ and the probability of $n$ 1's is also $\frac{1}{2^n}$. So the probability that there's at least one of each is just $1  \frac{1}{2^{n1}}$. Now you just have to find the $n$ for which $1  \frac{1}{2^{n1}} \ge .99$. Then $.01 \ge \frac{1}{2^{n1}}$ and $n = 8$. 

Tags 
probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Continuous probability; find probability density function  rivaaa  Advanced Statistics  5  November 5th, 2015 01:51 PM 
probability set theory  probability of x out of n events  hbonstrom  Applied Math  0  November 17th, 2012 07:11 PM 
Joint probability density function, probability  token22  Advanced Statistics  2  April 26th, 2012 03:28 PM 
Probability (probability mass function,pmf)  naspek  Calculus  1  December 15th, 2009 01:18 PM 