Question

example 1: patricia rolls two standard number cubes. use the table given to find the sample space, then find the probability that the sum of the numbers she rolls is 9
$=\frac{1}{9}$

example 2: at the ice cream shop, customers can choose one type of cone (waffle or sugar), one flavor of ice cream (chocolate, vanilla or strawberry), and one type of sprinkles (rainbow or chocolate). use a tree diagram to show the sample space and then find the probability of choosing an ice cream at random and getting a waffle cone with vanilla ice cream and rainbow sprinkles.

example 3: henry flips a coin 3 times. make a list to show the sample space, then find the probability of getting three heads.

Explanation:

Step1: Solve Example 1

First, define the sample space for two 6-sided dice: there are $6 \times 6 = 36$ total outcomes.
Identify pairs that sum to 9: $(3,6), (4,5), (5,4), (6,3)$ → 4 favorable outcomes.
Probability = $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{4}{36} = \frac{1}{9}$

Step2: Solve Example 2

Calculate total sample space: 2 cones × 3 flavors × 2 sprinkles = $2 \times 3 \times 2 = 12$ total outcomes.
There is 1 favorable outcome: (waffle cone, vanilla, rainbow sprinkles).
Probability = $\frac{1}{12}$

Step3: Solve Example 3

List the sample space for 3 coin flips:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} → 8 total outcomes.
There is 1 favorable outcome (HHH).
Probability = $\frac{1}{8}$

Answer:

Example 1: $\frac{1}{9}$
Example 2: $\frac{1}{12}$
Example 3: $\frac{1}{8}$