Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
At what angle should you throw something to maximise the distance it travels?
Two cannons are fired at one another and the cannonballs collide... what can you deduce?
This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
Exponential functions grow pretty quickly...
After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?
Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?
