en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Word Problems >

single die is rolled twice. Find the probability of getting a 3 the first time and 3 the second time. Express the probability as a simplified fraction.

Solution

s in g l e d i e i s ro ll e d tw i ce . F in d t h e p ro babi l i t y o f g e tt in g a 3 t h e f i rs t t im e an d 3 t h e seco n d t im e . E x p ress t h e p ro babi l i t y a s a s im pl i f i e d f r a c t i o n .

Solution

\frac{1}{36}

+1

Decimal

0.02777 \dots

Solution steps

Find the probability of getting a 3 the first time:

\frac{1}{6}

Find the probability of 3 the second time.:

\frac{1}{6}

Since the events are independent, Use the formula

P (X_{1} \land X_{2} \land \dots \land X_{k}) = P (X_{1}) \cdot P (X_{2}) \cdot \dots \cdot P (X_{k})

= \frac{1}{6} \cdot \frac{1}{6}

\frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}

= \frac{1}{36}

Popular Examples

What is the probability that a card drawn randomly from a standard deck of 52 cards is a two? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.The area of a circle is 81pi mm^2. What’s its circumference?find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is greater than 9, given that neither die is a six The area of a circle is 81𝜋 square feet. What is the circumference?The area of a circle is 0.0314 square miles. What is the circle's radius