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If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of getting exactly 1 six?

Solution

If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of getting exactly 1 six?

Solution

\frac{3125}{7776}

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 = 5

number of successes

x = 1

probability of success in any one trial

p = \frac{1}{6}

P (1) = 5 C 1 \cdot (\frac{1}{6})^{1} (1 - \frac{1}{6})^{5 - 1}

5 C 1 = 5

= 5 (\frac{1}{6})^{1} (\frac{5}{6})^{4}

5 (\frac{1}{6})^{1} (\frac{5}{6})^{4} = \frac{3125}{7776}

= \frac{3125}{7776}

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