Chapter 6.3, Problem 4.2CYU

To determine

To find: The probability T is equal to 3.

Answer to Problem 4.2CYU

The probability is 0.116.

Explanation of Solution

Given:

There are two pairs of dice which are being rolled to get doubles.

The variable T shows the number of rolls dice take.

Concept used:

The pdf of geometric distribution is:

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

Calculation:

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

  $P\left(T=3\right)$

is computed as:

  $\begin{array}{c}P\left(T=3\right)={\left(1-\frac{1}{6}\right)}^{3-1}\left(\frac{1}{6}\right)\\ ={\left(\frac{5}{6}\right)}^2\times \frac{1}{6}\\ =0.116\end{array}$

Thus, the probability is 0.116.

Interpretation:

There are 11.6% chances that dice would be rolled thrice to get the doubles.