A family has 6 children. I've figured out that there are 64 different ways the genders of the kids can work out. What's the probability that there's at least 1 boy in the family?

1 Answer
MathFact-orials.blogspot.com
Oct 25, 2016

#63/64=.984375#

Explanation:

Let's look at the problem this way:

Each child has a 50/50 shot of being a boy/girl, which is how you arrived at the total number of ways this can work out is #2^6=64#. "How many of those scenarios have at least 1 boy" is one way of looking at the question. Another way is to list out all the possibilities where there are no boys, subtract those scenarios away, and then you know what you have left has at least one boy.

So the scenarios with no boys at all is 1. Meaning all the other 63 do have at least one boy.

The probability therefore for having at least one boy is:

#63/64=.984375#

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