Question

two dice are rolled one after the other. construct a sample space and determine the probability that the sum of the dots on the dice total 9.

the probability that the sum of the dots on the dice total 9 is .
(type an integer or a simplified fraction.)

Explanation:

Determine the size of the sample space

Using the Sample Space Construction knowledge point

$$ N = 6 \times 6 = 36 $$

Identify the favorable outcomes

Using the Theoretical Probability knowledge point

$$ E = \{(3,6), (4,5), (5,4), (6,3)\} $$

$$ n(E) = 4 $$

Calculate the probability

Using the Theoretical Probability knowledge point

$$ P(\text{sum is } 9) = \frac{n(E)}{N} = \frac{4}{36} $$

Simplify the fraction

Using the Fraction Simplification knowledge point

$$ P(\text{sum is } 9) = \frac{1}{9} $$

Answer:

Two dice are rolled one after the other. Construct a sample space and determine the probability that the sum of the dots on the dice total 9.

The probability that the sum of the dots on the dice total 9 is <blank>\(\frac{1}{9}\)</blank>.
(Type an integer or a simplified fraction.)