If a six sided die is rolled six times, what is the probability that the number1 was rolled exactly once?

解

I f a s i x s i d e d d i e i s ro ll e d s i x t im es, w ha t i s t h e p ro babi l i t y t ha t t h e n u mb er 1 w a s ro ll e d e x a c tl y o n ce ?

\frac{3125}{7776}

十進法表記

0.40187 \dots

解答ステップ

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 = 6

number of successes

x = 1

probability of success in any one trial

p = \frac{1}{6}

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

6 C 1 = 6

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

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

= \frac{3125}{7776}