Question

Suppose you roll a pair of fair, six-sided dice until you get doubles. Let $T=$the number of rolls it takes.

In the game of Monopoly, a player can get out of jail free by rolling doubles within $3$turns. Find the probability that this happens

Short answer

The probability is$0.4213$.

Step-by-step solution

Given Information

Given that there are two pairs of dice that are being rolled to get doubles.

The variable T shows the number of rolls dice take.

Calculation

The pdf of geometric distribution is:

$$\begin{gathered} P(X=k) \\ =(1-p{)}^{k-1}p \end{gathered}$$

The probability of success $\frac{1}{6}$.

The probability using $\mathrm{Ti}-83$plus calculator can be calculated as