What is the probability of not rolling a five on either die when rolling two six-sided dice?

What is the probability of not rolling a five on either die when rolling two six-sided dice?

• A. 1/36
• B. 1/6
• C. 4/36
• D. 25/36

Answer: (D)

To determine the probability of not rolling a five on either die when rolling two six-sided dice, first consider the total possible outcomes when rolling the two dice. Each die has six faces, so there are \(6 \times 6 = 36\) total outcomes. Next, we focus on the number of outcomes that do not result in a five on either die. Each die has five outcomes that are not a five: \(1, 2, 3, 4, \text{and } 6\). Therefore, for each die, there are five favorable outcomes. When rolling two dice, the outcomes for the first die can pair with any of the outcomes for the second die. Thus, the total number of favorable outcomes where neither die shows a five is \(5 \times 5 = 25\). Now, to find the probability of not rolling a five on either die, we take the number of favorable outcomes (where neither die shows a five) and divide by the total number of outcomes: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{25}{36} \] This fraction represents the probability of the event

To determine the probability of not rolling a five on either die when rolling two six-sided dice, first consider the total possible outcomes when rolling the two dice. Each die has six faces, so there are (6 \times 6 = 36) total outcomes.

Next, we focus on the number of outcomes that do not result in a five on either die. Each die has five outcomes that are not a five: (1, 2, 3, 4, \text{and } 6). Therefore, for each die, there are five favorable outcomes.

When rolling two dice, the outcomes for the first die can pair with any of the outcomes for the second die. Thus, the total number of favorable outcomes where neither die shows a five is (5 \times 5 = 25).

Now, to find the probability of not rolling a five on either die, we take the number of favorable outcomes (where neither die shows a five) and divide by the total number of outcomes:

[

\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{25}{36}

]

This fraction represents the probability of the event