If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 0 sixes?

Решение

I f a f ai r d i e i s ro ll e d 3 t im es, w ha t i s t h e p ro babi l i t y, t o t h e n e a res t t h o u s an d t h, o f g e tt in g e x a c tl y 0 s i x es ?

\frac{125}{216}

десятичными цифрами

0.57870 \dots

Шаги решения

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 = 3

number of successes

x = 0

probability of success in any one trial

p = \frac{1}{6}

P (0) = 3 C 0 \cdot (\frac{1}{6})^{0} (1 - \frac{1}{6})^{3 - 0}

3 C 0 = 1

= 1 \cdot (\frac{1}{6})^{0} (\frac{5}{6})^{3}

1 \cdot (\frac{1}{6})^{0} (\frac{5}{6})^{3} = \frac{125}{216}

= \frac{125}{216}