In a game, two dice are rolled per turn. On average, how many turns will a player be expected to take to get at least one 4 shown on one of the dice?
On average it'll take 3 throws to roll a 4.
Let's think of this in this way - each throw of the two dice will have some chance of having a 4 shown on at least one of the dice. And so we need to keep throwing dice (add the probabilities for each throw) until we have a probability of one or more - "certitude" that we'll have thrown at least one 4.
The probability for one die to have a 4 show up is
And so on average it'll take 3 throws to roll a 4.