en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Word Problems >

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

Solution

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 ?

Solution

\frac{3125}{7776}

+1

Decimal

0.40187 \dots

Solution steps

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}

Popular Examples

find the two smallest consecutive even integers whose sum is at least 51 Suppose that when your friend was born, your friend's parents deposited 9000 in an account paying 5.1% interest compounded quarterly. What will the account balance be after 15 years?The radius of a circle is 19 cm. Find its circumference in terms of pipi.bob has 10 apples. He shoves 5 up his butt. How many does he have left?The product of a number and 9 less than the number is 36. Find the number