Question

jewels spins the pointer of a spinner the spinner has 7 equal side section labeled 1 to 7

create a probability model for the spinner

Answer 1

To create a probability model for a spinner with 7 equal sections labeled from 1 to 7, we will first outline the sample space and then determine the probability of each outcome.

### Sample Space
The sample space \( S \) for the spinner consists of the possible outcomes when the spinner is spun. In this case, the outcomes are:

\[
S = \{1, 2, 3, 4, 5, 6, 7\}
\]

### Probability of Each Outcome
Since the spinner has 7 equal sections, each section has an equal probability of landing when the spinner is spun. The total number of outcomes is 7. Therefore, the probability \( P \) of landing on each individual section can be calculated as follows:

\[
P(i) = \frac{1}{\text{Total Number of Outcomes}} = \frac{1}{7}
\]

for each \( i \in \{1, 2, 3, 4, 5, 6, 7\} \).

### Probability Model
The probability model for the spinner can be presented as follows:

\[
\begin{align*}
P(1) &= \frac{1}{7} \\
P(2) &= \frac{1}{7} \\
P(3) &= \frac{1}{7} \\
P(4) &= \frac{1}{7} \\
P(5) &= \frac{1}{7} \\
P(6) &= \frac{1}{7} \\
P(7) &= \frac{1}{7} \\
\end{align*}
\]

### Summary
The probability model indicates that each number from 1 to 7 has an equal probability of \(\frac{1}{7}\) when the spinner is spun. The total probabilities sum up to 1, confirming it is a valid probability model:

\[
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) = \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} + \frac{1}{7} = 1
\]