Question

what is the probability of spinning a spinner with 2 equal - sized sections, blue and orange, and landing on orange and then rolling anything but a 4 on a standard number cube?
you can use the completed tree to find the probability of the spinner landing on blue, then rolling anything but a 4. start by finding the number of outcomes that show the spinner landing on blue, then rolling anything but a 4.
probability of landing on blue, then rolling anything but a 4:
\\(\frac{\text{number of desired outcomes}}{\text{number of total outcomes}} = \frac{\square}{?}\\)

Explanation:

Step1: Determine total outcomes

The spinner has 2 sections (blue, orange), and the cube has 6 faces. Total outcomes: \(2\times6 = 12\).

Step2: Find desired outcomes (blue, not 4)

Spinner on blue (1 way), cube not 4: 5 numbers (1,2,3,5,6). Desired outcomes: \(1\times5 = 5\).

Step3: Calculate probability

Probability = \(\frac{\text{Desired}}{\text{Total}}=\frac{5}{12}\). Wait, no—wait, the question for the blue then not 4: spinner blue (1 section), cube not 4 (5). Total spinner - cube outcomes: 26=12. Desired: 15=5? Wait, no, the spinner has 2 equal sections, so blue is 1 section. Cube: numbers 1 - 6, not 4: 5. So number of desired outcomes (blue, not 4) is 5? Wait, no, the tree: blue branch has 6 outcomes (1 - 6). Not 4: 5 (1,2,3,5,6). So desired outcomes for blue then not 4: 5. Total outcomes: 2*6=12. So the fraction is \(\frac{5}{12}\)? Wait, but the problem first asks about orange then not 4, but the box is for blue then not 4. Let's re - check.

For blue then rolling anything but 4:

• Spinner landing on blue: 1 outcome (since 2 equal sections: blue and orange, so blue is 1 out of 2, but in terms of combined outcomes with cube, each spinner outcome pairs with 6 cube outcomes. So blue has 6 cube outcomes (1 - 6).
• Rolling anything but 4: numbers 1,2,3,5,6: 5 outcomes.
• So number of desired outcomes (blue, not 4): 5.
• Total number of outcomes (spinner - cube): 2 (spinner) * 6 (cube) = 12.

So the fraction is \(\frac{5}{12}\), but the box is for the numerator (number of desired outcomes) first? Wait, the formula is \(\frac{\text{Number of desired outcomes}}{\text{Number of total outcomes}}\). The number of desired outcomes (blue, not 4) is 5, total outcomes is 12. But maybe the first box is the numerator (5) and the second is the denominator (12). Wait, the problem says "Number of desired outcomes" over "Number of total outcomes" equals [box] / [?]. So number of desired outcomes for blue then not 4: when spinner is blue, cube not 4: 5 (since cube has 6, minus 1 (the 4) gives 5). So the number of desired outcomes is 5, total outcomes is 12. So the first box (numerator) is 5, denominator is 12. But let's confirm:

Spinner: 2 sections (blue, orange). Each section has 6 cube outcomes. So total outcomes: 2*6 = 12.

For blue: 6 cube outcomes (1 - 6). Not 4: 5 (1,2,3,5,6). So desired outcomes (blue, not 4): 5.

So the fraction is \(\frac{5}{12}\), so the number of desired outcomes is 5, total is 12.

Answer:

The number of desired outcomes is 5, and the number of total outcomes is 12. So the fraction is \(\frac{5}{12}\), with the numerator (number of desired outcomes) being 5.