$\textbf{Red Cards}$
There are $7$ cards. Two of them have both sides red, two of them have both sides black, the rest three have one side red and one side black. Joe draws one card randomly and finds one side is red, what is the probability that the other side is red too?
$\textbf{Answer}$
$\frac{4}{7}$.
$\textbf{Analysis}$
This is a tricky question. Many people will give an answer of $\frac{2}{5}$. However, it is incorrect. Mathematically, this problem is a conditional probability. In plain English, given that the card has at least one red side, it is more likely that its both sides are red.
One intuitive way to explain the result is to disintegrate these seven double-sided cards into fourteen single-sided cards. Then the chance of getting each single-sided card is the same. Given that we know one side is red, this red card must be among the seven red single-sided cards each of which has the same chance to be chosen. When we map these single-sided cards back to the original double-sided cards, we will find that these two double-red cards have double chances than the single-red cards to be picked up given a red single-sided card is chosen.. Therefore, the result is $\frac{4}{7}$.
$\textbf{Note}$
This type of problems have strong relation to math. Thus, they are frequently used by technology related companies in their interviews.