Question

complete each sentence to make a true statement.
the theoretical probability of rolling a 2 on a single roll of a number cube is 2/6
the theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue, 1 red, and 1 orange section is

Explanation:

Step1: Calculate probability of rolling a 2

A standard number cube has 6 faces. The probability of rolling a specific number (in this case, 2) is calculated by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (rolling a 2) is 1, and the total number of outcomes is 6. So the probability is \(\frac{1}{6}\). But if we consider the fraction \(\frac{2}{6}\), it can be simplified to \(\frac{1}{3}\), which is incorrect for rolling a single - specific number on a standard 6 - faced cube. However, if we assume a non - standard interpretation (but based on the given \(\frac{2}{6}\) in the problem context), we just note the structure.

Step2: Calculate probability of spinner landing on blue

The spinner has 4 equal - sized sections (1 purple, 1 blue, 1 red, 1 orange). Using the probability formula \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), the number of favorable outcomes (landing on blue) is 1, and the total number of outcomes is 4. So the probability is \(\frac{1}{4}\).

Answer:

The theoretical probability of rolling a 2 on a single roll of a number cube is \(\frac{1}{6}\). The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue, 1 red, and 1 orange section is \(\frac{1}{4}\).