Use the binomial distribution to find the probability that five rolls of a fair die will show exactly two threes. Express your answer as a decimal rounded to 1 decimal place.

Solution

Solution

\frac{625}{3888}

Solution steps

Probability of 3 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 = 2

probability of success in any one trial

p = \frac{1}{6}

P (2) = 5 C 2 (\frac{1}{6})^{2} (1 - \frac{1}{6})^{5 - 2}

5 C 2 = 10

= 10 (\frac{1}{6})^{2} (\frac{5}{6})^{3}

10 (\frac{1}{6})^{2} (\frac{5}{6})^{3} = \frac{625}{3888}

= \frac{625}{3888}

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