Question

what is the probability of spinning a spinner with 2 equal - sized sections, blue and orange, and landing on orange and then rolling a 5 on a standard number cube?
now, use the completed tree to find the probability of spinning the spinner and landing on orange, then rolling a 5. start by finding the number of outcomes that show landing on orange, then rolling a 5.
probability of landing on orange, then rolling a 5:
\\(\frac{\text{number of desired outcomes}}{\text{number of total outcomes}} = \frac{\square}{?}\\)

Explanation:

Step1: Determine spinner outcomes

The spinner has 2 equal sections (blue, orange), so P(orange) = $\frac{1}{2}$.

Step2: Determine cube outcomes

A standard cube has 6 faces, so P(rolling 5) = $\frac{1}{6}$.

Step3: Find combined probability

For independent events, multiply probabilities: $\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$.

Step4: Count outcomes (tree method)

• Total outcomes: Spinner (2) × Cube (6) = 12.
• Desired outcomes: 1 (orange then 5).
• So $\frac{\text{Desired}}{\text{Total}} = \frac{1}{12}$.

Answer:

$\frac{1}{12}$