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Rolling a die 4 times. What is the probability of rolling a 1 twice?

Solución

Rolling a die 4 times. What is the probability of rolling a 1 twice?

Solución

\frac{25}{216}

Pasos de solución

Probability of 1 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 = 4

number of successes

x = 2

probability of success in any one trial

p = \frac{1}{6}

P (2) = 4 C 2 (\frac{1}{6})^{2} (1 - \frac{1}{6})^{4 - 2}

4 C 2 = 6

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

6 (\frac{1}{6})^{2} (\frac{5}{6})^{2} = \frac{25}{216}

= \frac{25}{216}

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