Question

identifying theoretical probability
complete each sentence to make a true statement.
the theoretical probability of rolling a 2 on a single roll of a number cube is
the theoretical probability of landing on blue on a single spin of a spinner with 1 blue section, 1 red, and 1 orange
section is
6
2/6
1/6
0

Explanation:

Step1: Calculate probability of rolling a 2 on a number cube

A standard number cube has 6 faces numbered from 1 - 6. The formula for theoretical probability \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). For the event of rolling a 2, the number of favorable outcomes \(n = 1\) (since there is only one face with the number 2) and the total number of outcomes \(N=6\). So \(P(\text{rolling a }2)=\frac{1}{6}\).

Step2: Assume spinner details (though not fully shown, but for landing on blue, if we assume a fair spinner with say 6 equal - colored sections and 2 of them are blue)

Using the probability formula \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). If the number of blue - colored sections \(n = 2\) and the total number of sections \(N = 6\), then \(P(\text{landing on blue})=\frac{2}{6}\).

Answer:

The theoretical probability of rolling a 2 on a single roll of a number cube is \(\frac{1}{6}\). (Assuming a fair 6 - faced cube). For the spinner (assuming 6 sections with 2 blue), the theoretical probability of landing on blue is \(\frac{2}{6}\)