This is a very famous and much discussed problem.
It is not easy to understand its solution.
But here is the solution.
Can someone explain the maths involved in being able to solve this to me please:
Every packet of Captain Crunch Chips comes with a randomly inserted letter: C, H, I, or P. If you can collect one of each letter, you will win a free packet of chips. Each letter is equally likely, what is the expected number of chip packets you need to open to win a free packet?
I can find the probability of getting it in four goes, and five etc with work (probably do a probability tree). And have used a quick simulation to get a result of 7.4, but am sure that there must be a systematic way to solve it. Would also like to then be able to generalize it to a problem that would have more than 4 possible picks etc.
Thanks
This is a very famous and much discussed problem.
It is not easy to understand its solution.
But here is the solution.