Chapter 12.5, Problem 10PPS

To determine

To state whether the events are independent or dependent find the probability.

Answer to Problem 10PPS

The event is independent and the probability of not getting the same number twice is $\frac{5}{36}\text{ or 13}\text{.88\%}$ .

Explanation of Solution

Given information:

The given statement is:

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

Formula used:

The following formula is used:

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

Calculation :

The result of one rolling does not affect the result of another, so it is an independent event.

The probability of getting two different numbers can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{getting a number}\right)=\frac{1}{6}\\ \text{P}\left(\text{not getting the number}\right)=\frac{5}{6}\\ \text{P}\left(\text{not getting the same number twice}\right)=\frac{1}{6}\times \frac{5}{6}\\ \text{P}\left(\text{not getting the same number twice}\right)=\frac{5}{36}\text{ or 13}\text{.88\%}\end{array}$

Hence, the event is independent and the probability of not getting the same number twice is $\frac{5}{36}\text{ or 13}\text{.88\%}$ .