Hi friends,

I am a machine learning and data science enthusiast. I love playing with numbers and finding insights. I know many of you are, at least to some level. Even if you are not but you have some level of interest in mathematics, there is a great chance you will find this post interesting.

Please let me know if you guys already knew this and if there are many more which I should check out, please let me know in the comments belows. I encourage all my fellow reader to read them too.

I like solving problems, sometimes I find it on renowned platforms like Kaggle and hackerearth. Randomly I came across this seemingly easy question but which blew my mind off [partly because I feel this problem is not articulated well!]

I thought I didn't have to think much about it. Because it is just so straight forward. I mean it is given that one child is a boy, only probability of the other child being a boy is 1/2 [unless otherwise stated].

I selected the 1/2 answer from the answer, it was a wrong one. Okay, it needed a little more thinking. I wrote down all the possibilities at least one of the child is a boy [we are already given this information].

[BB, BG, GB]

Therefore, another answer which is also equally likely according to the question is 1/3. And as it turns out, this indeed is a correct answer.

But how can we have two equally correct answers for this. In my view, both the answers, as per the problem statement is correct.

I took to Google for adjudication, and again, Google didn't disappoint. Look what I found:

Boy or Girl paradox

The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, Mr. Smith's Children and the Mrs. Smith Problem. The initial formulation of the question dates back to at least 1959, when Martin Gardner featured it in his October 1959 "Mathematical Games column" in Scientific American. He titled it The Two Children Problem, and phrased the paradox as follows:

• Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
• Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

View on Wikipedia

I think it is a good read. I suggest you all to go through it (if you already haven't).

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