# CTK Insights

• ## Pages

20 May

### Probabilities in a Painted Cube

Now generalize: cut the cube into nxnxn smaller cubes and ask the same question. The problem is not awfully difficult but needs some figuring out. Following the foregoing pattern, we eventually arrive at 1/n. But here is a delightful shortcut

13 Jan

### A Pair of Probability Games for Beginners

The second problem is subtler and sounds rather deceptive: of $6$ possible outcomes of one throw of a single die, $2$ or $5$ come up with the probability of $\displaystyle\frac{1}{3} \lt \frac{1}{2}$. However, the situations changes drastically when two dice are tossed

06 Feb

### Mediant Fractions and Simpson's Paradox

TweetGiven two fractions a/b and c/d, the mediant of the two is defined as the fraction (a + c)/(b + d). Many would point to the mediant fraction as a dangerous concept that is bound to confuse students who often quite innocently produce it adding up to fractions. However, the mediant has its uses and […]

09 Nov

### Naturally Random Numbers

TweetAlbert Einstein's dictum "God does not play dice" is a concise expression of determinism - the belief that the past fully determines the future. Had it been possible to write down all the required equations and feasible to solve them, we would have had a complete picture of the future. Quantum mechanics recognized randomness as […]