# 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.

#### 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 $\frac{1}{6}$ and so the probability for two dice is $\frac{1}{6} + \frac{1}{6} = \frac{1}{3}$.

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

$\frac{1}{3} x \ge 1$

$x \ge 3$

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