Yvonne Scott posted the following question:
Stuart Price noted that the answer to the last part can be obtained as the answer to part (iii) divided by the answer to part (iv), by the definition of conditional probability.
But if we think about what’s going on a little further, we will be able to understand the structure of this problem more and see further connections.
One of my UKMT Mentoring scheme mentees was asking me about induction, and we were discussing how strong induction and ordinary induction are related to each other. In the end, I ended up writing this piece, which I’m sharing here for general interest.
I’ve been thinking about implicit differentiation with my colleagues recently. How do we teach it (at high school level), and what subtleties are involved? It started by trying to understand what we mean by the equation
\begin{equation} \frac{dy}{dx}=1\biggm/\frac{dx}{dy}. \label{eq:recip} \end{equation}
Some questions raised by this include:
(a) What does this equation mean?
(b) How can we explain this to students and also why it is true?
(c) Where would this result be useful to them (besides in artificial exam questions)?
In this post, I will offer some thoughts on (a) and (b), but I’m still fairly stuck on (c).