Use the sample space shown in the figure to find the probability for the experiment of rolling a pair of dice. (Enter the probability as a fraction.) $P($ four or six

Step 1 ：The problem is asking for the probability of rolling a pair of dice and getting a sum of either four or six.

Step 2 ：To solve this, we need to know the total number of outcomes when rolling two dice and the number of outcomes that result in a sum of four or six.

Step 3 ：The total number of outcomes when rolling two dice is \(6 * 6 = 36\) because each die has 6 faces.

Step 4 ：The outcomes that result in a sum of four are: (1,3), (2,2), (3,1). So there are 3 outcomes.

Step 5 ：The outcomes that result in a sum of six are: (1,5), (2,4), (3,3), (4,2), (5,1). So there are 5 outcomes.

Step 6 ：So the probability is the number of favorable outcomes divided by the total number of outcomes.

Step 7 ：\(\text{total outcomes} = 36\)

Step 8 ：\(\text{favorable outcomes} = 8\)

Step 9 ：\(\text{probability} = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{8}{36}\)

Step 10 ：Final Answer: The probability of rolling a pair of dice and getting a sum of either four or six is \(\boxed{\frac{2}{9}}\).