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If a fair die is rolled 7 times, what is the probability, to the nearest thousandth, of getting exactly o fours?
Answer:

If a fair die is rolled $7$ times, what is the probability, to the nearest thousandth, of getting exactly o fours? $\newline$ Answer:

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Full solution

Q. If a fair die is rolled

7

times, what is the probability, to the nearest thousandth, of getting exactly o fours?

\newline

Answer:

Understand the problem: Understand the problem. $\newline$ We need to calculate the probability of not rolling a $4$ in any of the $7$ rolls of a fair six-sided die.
Calculate single roll probability: Calculate the probability of not rolling a four on a single roll. $\newline$ A fair die has six sides, so the probability of rolling any specific number, like a four, is $\frac{1}{6}$ . Therefore, the probability of not rolling a four is $\frac{5}{6}$ .
Calculate probability in all rolls: Calculate the probability of not rolling a four in all seven rolls. $\newline$ Since each roll is independent, we multiply the probability of the event not happening in a single roll by itself seven times. $\newline$ $(\frac{5}{6}) ^ 7$
Perform the calculation: Perform the calculation. $\newline$ $(\frac{5}{6}) ^ 7 \approx 0.279$
Round the result: Round the result to the nearest thousandth. $\newline$ The probability, to the nearest thousandth, of not rolling a four in seven rolls is approximately $0.279$ .

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