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If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 0 sixes?

Solution

If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 0 sixes?

Solution

\frac{125}{216}

Solution steps

Probability of 6 when a die is rolled:

\frac{1}{6}

For multiple independent trials

P (x) = n C x \cdot p^{x} \cdot (1 - p)^{n - x}

number of trials

n = 3

number of successes

x = 0

probability of success in any one trial

p = \frac{1}{6}

P (0) = 3 C 0 \cdot (\frac{1}{6})^{0} (1 - \frac{1}{6})^{3 - 0}

3 C 0 = 1

= 1 \cdot (\frac{1}{6})^{0} (\frac{5}{6})^{3}

1 \cdot (\frac{1}{6})^{0} (\frac{5}{6})^{3} = \frac{125}{216}

= \frac{125}{216}

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