Answer:
[tex]\dfrac{1}{216}[/tex]
Step-by-step explanation:
In Katie's simulation, a roll of 1 represents staying after school, while rolls of 2, 3, 4, 5, or 6 represent leaving school at the end of classes. Thus,
- the probability of staying at school [tex]=\frac{1}{6}[/tex] (only one of six possible outcomes is favorable)
- the probability of leaving school [tex]=\frac{5}{6}[/tex] (five of six possible outcomes are favorable)
The probability that three randomly chosen students will all stay after school for extracurricular activities today is
[tex]\dfrac{1}{6}\cdot \dfrac{1}{6}\cdot \dfrac{1}{6}=\dfrac{1}{216}[/tex]
