Question

what is the probability of spinning a spinner with 2 equal - sized sections, blue and orange, and landing on orange and then rolling either a 2 or a 5 on a standard number cube?
use the completed tree to find the probability of spinning the spinner and landing on orange, then rolling either a 2 or a 5. start by finding the number of desired outcomes in this experiment.

probability of landing on orange, then rolling either a 2 or 5:
\\(\frac{\text{number of desired outcomes}}{\text{number of total outcomes}} = \frac{\square}{?}\\)

Explanation:

Step1: Find total outcomes

Spinner has 2 sections, cube has 6 faces. Total outcomes: \(2\times6 = 12\).

Step2: Find desired outcomes

Spinner lands on orange (1 way), cube lands on 2 or 5 (2 ways). Desired outcomes: \(1\times2 = 2\).

Step3: Calculate probability

Probability = \(\frac{\text{Desired}}{\text{Total}}=\frac{2}{12}=\frac{1}{6}\). Wait, no—wait, total outcomes: each spinner outcome (2) with 6 cube, so 12. Desired: orange (1 spinner path) with 2 (2 or 5) cube, so 2. Wait, but let's recheck. Spinner: orange is 1 branch, then cube has 6. Blue is another. So total outcomes: 2 (spinner) 6 (cube) = 12. Desired: orange (1) 2 (2 or 5) = 2. So probability is \( \frac{2}{12} = \frac{1}{6} \)? Wait, no—wait, the tree: orange has 6 branches (1 - 6), blue has 6. So total outcomes: 6 + 6 = 12. Desired: orange - 2 and orange - 5: 2 outcomes. So number of desired is 2, total is 12. So \( \frac{2}{12} = \frac{1}{6} \)? Wait, but let's do it step by step.

First, probability of orange on spinner: \( \frac{1}{2} \). Probability of 2 or 5 on cube: \( \frac{2}{6} = \frac{1}{3} \). Then multiply: \( \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \). Which matches \( \frac{2}{12} \) (since 2 desired, 12 total). So the number of desired outcomes is 2, total is 12, so \( \frac{2}{12} = \frac{1}{6} \). Wait, but the question is asking for the fraction \( \frac{\text{Number of desired}}{\text{Total}} \), so the numerator is 2, denominator 12, simplifies to \( \frac{1}{6} \). But let's check the tree: orange has 6 branches (1,2,3,4,5,6), blue has 6. So desired are orange-2 and orange-5: 2 outcomes. Total outcomes: 6 (orange) + 6 (blue) = 12. So \( \frac{2}{12} = \frac{1}{6} \).

Answer:

\(\frac{1}{6}\)