MATM Appendix: Boy born on a Tuesday

During Maths at the Movies: The Imitation Game Ben introduced the
following puzzle:




I have two children. One of them is a boy.

What is the probability that both children are boys? 





Although counter-intuitive, it can be shown that the solution is
1/3.





He also posed a similar, but different question:





I have two children. One of them is a boy who was born on a
Tuesday.

What is the probability that both children are boys?





Although very similar, the answer turns out to be 13/27, which is
quite different. However, Ben got confused when giving the answer
during our pi podcast and paid penance by making a video


 





However, there is still some debate about the answer.





Join us this week as we record all from the same location and try
and tease apart the complexity of weird conundrum.






Yup, we really are altogether!