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Popular Word Problems >

A die is tossed 3 times. What is the probability as a decimal of no fives turning up?

Solution

A d i e i s t osse d 3 t im es . Wha t i s t h e p ro babi l i t y a s a d ec ima l o f n o f i v es t u r nin g u p ?

Solution

\frac{125}{216}

+1

Decimal

0.57870 \dots

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 = 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}

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