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a fair die is rolled $3$ times, what is the probability, of getting exactly $0$ sixes?

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Theoretical probability

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Q. a fair die is rolled

3

times, what is the probability, of getting exactly

0

sixes?

Calculate Probability: Calculate the probability of not rolling a six on a single roll. $\newline$ P(Not rolling a six) = $\frac{5}{6}$ , because there are $5$ outcomes that are not a six out of $6$ possible outcomes.
Multiply Probabilities: Since the die rolls are independent, multiply the probability of not rolling a six for each of the three rolls. $\newline$ P(Exactly zero sixes in $3$ rolls) = $(\frac{5}{6}) \times (\frac{5}{6}) \times (\frac{5}{6})$
Perform Multiplication: Perform the multiplication to find the probability. $P(\text{Exactly zero sixes in 3 rolls}) = \frac{125}{216}$

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