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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: 1,572 Thanks: 379 
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 $n = 8$. 

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