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If a fair die is rolled 6 times, what is the probability, to the nearest thousandth, of getting exactly 2 fives?

Solution

If a fair die is rolled 6 times, what is the probability, to the nearest thousandth, of getting exactly 2 fives?

Solution

\frac{3125}{15552}

Solution steps

Probability of 5 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 = 6

number of successes

x = 2

probability of success in any one trial

p = \frac{1}{6}

P (2) = 6 C 2 (\frac{1}{6})^{2} (1 - \frac{1}{6})^{6 - 2}

6 C 2 = 15

= 15 (\frac{1}{6})^{2} (\frac{5}{6})^{4}

15 (\frac{1}{6})^{2} (\frac{5}{6})^{4} = \frac{3125}{15552}

= \frac{3125}{15552}

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