Probability of Simple Events
The probability of an event occurring is somewhere between impossible (0) and certain (1)...the
greater the number the greater the likelihood of the event occurring.
Key Concept: The probability of an event is a ratio that compares the number of favorable
outcomes to the number of possible outcomes.
P(event) = Number of favorable outcomes
Number of possible outcomes
Probability can be written as a fraction, decimal or percent
Examples:
Find the probability of rolling a 4 on the number cube
Find the probability of rolling a 4,5 or 6
What is the P(4)?
What is the P(4,5 or 6)?
There is only one 4 on the number cube
P(4) = Number of favorable outcomes
Number of possible outcomes
P(4)=
P(4) is
The word or indicates that the number of
favorable outcome must include 4 5 and 6.
P(4,5 or 6) =
3 1

6 2
1
1
6
P(4,5 or 6) is 2 , 50%, or 0.50
1
, or about 17%, or about 0.17
6
Finding Probability of the Complement
Complementary event are two events in which one or the other occurs but they cannot happen at
the same time. The sum of an event and its complement is 1 or 100%
Find the probability of not rolling a 4 in Example 1.
The probability of not rolling a 4 and rolling a 4 are complementary. So the sum of the probabilities
must equal 1.
P(4) + P(not 4) = 1
1
+ P(not 4)=1
6
Think…
1
plus what number equals 1
6
P(not 4) =
5
or about 83% or about 0.83
6
The spinner shown is spun once. Find the probability of each event.
Write each answer as a fraction, percent and decimal.
1. P(multiple of 4) __________
2. P(1,3,5) ___________
___________
___________
___________
___________
3. P(not a factor of 6) __________ ___________
___________
4. P(white or black) ___________
___________
___________
5. The probability of spinning the number 2 is 12.5%. Describe the complement of this event and
finds its probability. _____________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
A letter tile is chosen randomly. Find the probability of each
event. Write each answer as a fraction, percent and decimal.
6. P(D) ______________
_______________
_____________
7. P(vowel) ____________ _______________
______________
8. P(not E) ____________ _______________
______________
9. P(N, M, R or I) ___________
____________ ____________
10. Write an event where the probability would be greater than 50%. ______________________________
__________________________________________________________________________________________________
11. Determine P(2) and P(1) for the spinner. Write the probabilites
as fractions, decimals and percents.
2
3
1
4
12. Determine P(not 4).
13. A bag contains 6 black, 4 yellow and 8 blue marbles. How many marbles of each color should
be added so that the total number of marbles is 27, but the probability of randomly selecting one
marble of each color remains unchanged?
14. The probability of choosing a marble with the color red is 12/1000. Find the probability of not
choosing red. Then describe the likelihood of the event occurring.