Question

the table below shows all of the possible outcomes for rolling two six - sided number cubes. table showing outcomes of rolling two six - sided number cubes what is the probability of rolling an even number first and an odd number second? options: 1/9, 1/8 (and other options not fully visible)

Explanation:

Step1: Identify total outcomes

There are \(6\times6 = 36\) total possible outcomes when rolling two six - sided cubes.

Step2: Identify favorable outcomes

Even numbers on the first cube: 2, 4, 6 (3 possibilities). Odd numbers on the second cube: 1, 3, 5 (3 possibilities).
For each even number on the first cube, there are 3 odd numbers on the second cube. So the number of favorable outcomes is \(3\times3=9\).

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{9}{36}=\frac{1}{4}\) (Wait, maybe there was a typo in the options. But following the steps: total outcomes 36, favorable 9. So \(P = \frac{9}{36}=\frac{1}{4}\). But if we re - check, even first (2,4,6) and odd second (1,3,5). For first = 2: (2,1),(2,3),(2,5); first = 4: (4,1),(4,3),(4,5); first = 6: (6,1),(6,3),(6,5). That's 9 outcomes. So probability is \(\frac{9}{36}=\frac{1}{4}\). But if the options have \(\frac{1}{4}\) (maybe the given options were mis - typed). But according to the calculation, the probability is \(\frac{1}{4}\).

Answer:

\(\frac{1}{4}\) (Assuming the correct option is \(\frac{1}{4}\) if it was a typo in the provided options. If we follow the steps, the probability is \(\frac{9}{36}=\frac{1}{4}\))