Math 8 Number of Outcomes and Probability Name______________________________ Block_______ Date____________________ Finding Number of Possible Outcomes
The Sweet Treats Shoppe offers single-scoop ice cream in chocolate, vanilla, or strawberry, and two types of
cones: regular or sugar. Draw a tree diagram to determine the number of different ice cream cones.
Flavor
Type of cones
Outcome
How many different outcomes could you have for choosing your ice cream cone? __________________
Fundamental
Counting Principle
says that to find how many possible outcomes you can have, multiply like this:
 # of choices  # of choices  ...
 #forof choices
item 1   for item 2   for item 2 
_______
•
________
= __________ possible outcomes
Examples:
1. Draw a tree diagram to determine the number of possible outcomes. Check your answer using
the Fundamental Counting Principle.
a. A penny, a nickel, and a dime are tossed.
b. A number cube is rolled and the dime is tossed.
2. Use the Fundamental Counting Principle to find the number of possible outcomes:
a. The day of the week is picked at random and a number cube is rolled.
b. A number cube is rolled three times.
c. There are 5 true-false questions on a history quiz.
d. A month of the year is picked at random and a coin is tossed.
Finding the PROBABILITY of a SINGLE Event
P (event) =
3. There are eight equally likely outcomes on the
spinner. Find the probability of spinning a six.
4. Using the same spinner, find the probability of
spinning a number less than four.
5. A number cube is rolled. Find the probability of each event. Write each answer as a fraction and percent.
a. P(3)
b. P(greater than 4)
c. P(even)
d. P(2 or a 5)
e. P(less than 3)
f.
P(odd)
Finding the PROBABILITY of COMPOUND, INDEPENDENT Event
One letter tile is selected and the spinner is spun. What is the probability that both will be a vowel?
Here, we need to work with two probabilities at the same time:

P (select a vowel from tiles) =

P (spin a vowel from the spinner) =
MULTIPLY both probabilities together to obtain the probability of getting a vowel from BOTH:

P (select vowel from BOTH tiles and spinner) =
6. Use the previous example to find each probability:
a. P(both letters are A’s) =
b. P(both are consonants) =
7. A penny is tossed and a number cube is rolled. Find each probability.
a. P(tails and 3) =
b. P(heads and odd) =
8. Mia makes 70% of her free throws. What is the probability that she will make her next two free throws?