To determine the probability of getting a 3 on a spinner that has six equal parts labeled from 1 to 6, we can follow these steps:
1. Calculate the Probability of a Single Event:
Each of the six parts on the spinner is equally likely to occur. Therefore, the probability of landing on any specific number, such as 3, in one spin is [tex]\(\frac{1}{6}\)[/tex].
2. Understand Independent Events:
When the spinner is spun twice, the outcome of the first spin does not affect the outcome of the second spin. This means the events are independent.
3. Calculate the Combined Probability:
To find the combined probability of two independent events occurring in succession, we multiply the probability of each individual event. Thus, the probability of getting a 3 on the first spin and a 3 on the second spin is:
[tex]\[
\text{Probability of getting a 3 on the first spin} \times \text{Probability of getting a 3 on the second spin}
\][/tex]
Using our values:
[tex]\[
\left(\frac{1}{6}\right) \times \left(\frac{1}{6}\right)
\][/tex]
4. Perform the Multiplication:
Multiply the fractions:
[tex]\[
\frac{1}{6} \times \frac{1}{6} = \frac{1 \times 1}{6 \times 6} = \frac{1}{36}
\][/tex]
Thus, the probability of spinning a 3 twice in a row is [tex]\(\frac{1}{36}\)[/tex].
[tex]\[
\boxed{\frac{1}{36}}
\][/tex]
