Question

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

Find $P(T=3)$. Interpret this result in context.

Short answer

$\text{There are}11.6\%\text{chances that dice would be rolled thrice to get the doubles.}$

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

We have the pdf of geometric distribution is:

$P(X=k)=(1-p{)}^{k-1}p$

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

$P(T=3)$

is computed as:

localid="1649854229329" $$\begin{gathered} P(T=3)={\left(1-\frac{1}{6}\right)}^{3-1}\left(\frac{1}{6}\right) \\ ={\left(\frac{5}{6}\right)}^2\times \frac{1}{6} \\ =0.116 \end{gathered}$$.