Chapter 12.5, Problem 12PPS

To determine

To state whether the probability is dependent or independent and find the probability.

Answer to Problem 12PPS

The events are independent and the probability of rolling the same number twice is $\frac{1}{36}\text{ or 2}\text{.8\%}$ .

Explanation of Solution

Given information:

The given statement is:

“A die is rolled twice. What is the probability of rolling the same numbers?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The outcome of one event does not affect the outcome of the other, so they are independent events.

The probability can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{a number}\right)=\frac{1}{6}\\ \text{P}\left(\text{same number}\right)=\frac{1}{6}\\ \text{P}\left(\text{same number, same number}\right)=\frac{1}{6}\times \frac{1}{6}\\ \text{P}\left(\text{same number, same number}\right)=\frac{1}{36}\text{ or 2}\text{.8\%}\end{array}$

Hence, the events are independent and the probability of rolling the same number twice is $\frac{1}{36}\text{ or 2}\text{.8\%}$ .