Question

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?

Answer 1

On average it'll take 3 throws to roll a 4.

Explanation:

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 `1/6` and so the probability for two dice is `1/6+1/6=1/3`.

Let's have `x` represent the number of throws to get to our probability of at least one, and so:

`1/3x>=1`

`x>=3`

And so on average it'll take 3 throws to roll a 4.