When Probability Broke All Boundaries…
This is a question originally meant to be a meme in reddit which I found in some YouTube channel. I was pretty stunned and the most surprising thing was that this came to my feed a day before my 12th board examinations. I remember explaining this to a bunch of my friends and almost all were so confused after seeing the solution. Here is the question:
Mary has 2 children. She tells you that one is a boy born on a Tuesday. What’s the probability the other child is a girl?
Let’s prove it. At the surface, it obviously makes no sense since how can the day determine the gender? But conditional probability is known for the chaos it creates in such topics of discussion.
All possible cases are:
Some might be wondering why I have considered the same case of boy and girl twice. Well, the question has never said whether the boy was born first or second so we need to consider both the cases.
Now let’s give a single digit code for the days to make the listing out of possibilities much easier and simpler to understand:
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0-Sunday
1-Monday
2-Tuesday
3-Wednesday
4-Thursday
5-Friday
6-Saturday
Taking this into consideration, here are the possibilities listed out:
You might wonder a blank space left in the second column. Well, if you fill that as well we get 2 similar cases since we already took B2B2 into account in the first column. Now out of these possibilities, the last 2 columns consists of the possibilities which are the favourable events for our experiment. So using,
Since P((other child is girl)∩(at least one child is boy born on a Tuesday)=14/27. And since P(at least one child born is a boy)=27/27,
P(Other child is girl | at least one child is boy born on a Tuesday)= 14/27.
Which corresponds to 51.8%. I know that many of you might not be able to digest the fact that the day a child is born is deciding the fate of the gender of the other child being born indirectly. This is one of those cases where conditional probability just seems so true to be wrong and at the same time does not make any sense for a non mathematician. I still don’t know how to react to this solution. Credits to those crazy mathematicians who discovered concepts like this for students like us to think about for days.
I had crazy experience of showing this to my friends and seeing soem totally confused, a few who just understood a bit and a few who never really cared. I believe whoever has read this post till here must lie in the first 2 categories or else you would have not even opened this post. Anyways that’s for today. Hope you enjoyed it and….
Thank You!…
