1. Probabilities of Disjoint and Overlapping Events
Standard(s) from Instructional Guide:
SDAP 3.2
Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven
Student Objective (s):
- Students will use data to estimate the probability of disjoint and overlapping future events by solving problems independently and demonstrating proficiency with 80% accuracy

2. Definitions:
Disjoint events – (mutually exclusive events) are events that have no outcomes in common.
Overlapping events – are events that have one or more outcomes in common.

3. Examples: Disjoint Events Event A: Roll a 2
Event B: Roll an odd number
Overlapping Events
Event A: Roll an even number
Event B: Roll a prime number
Event A
Event B
Event A 2
Event B

4. Tell whether the events are disjoint or overlapping
Tell whether the events are disjoint or overlapping. (Hint draw Venn diagram)
Roll a number cube.
Event A: Roll a number less than 4
Event B: Roll a 5
Randomly select a student.
Event A: Select an 8th grader.
Event B: Select a boy

5. Probability of Disjoint Events:
Event A: Roll a number less than 4
Event B: Roll a number greater than 4.
There are 6 possible outcomes. There are 5 favorable outcomes for the event A or B. So, P(A or B)=5/6. You can also find P(A or B) by finding the sum of the probability of event A and the probability of event B.
P(A or B) = P (A) + P (B)= 3/6 + 2/6 = 5/6
Event A
Event B 4

6. Sooooooooo:
If A and B are disjoint events,
P(A or B) = P (A) + P (B)

7. Practice Finding the Probability of Disjoint Events:
Fifty tickets are sold for a raffle. You buy 2 tickets, and your friend buys 3 tickets. One ticket is randomly chosen as the winning ticket. What is the probability that you or your friend wins the raffle?
The events are disjoint b/c you and your friend can not both win.
Event A: You win
Event B: Your friend wins
P( A or B) = P (A) + P (B)
2/ /50 = 5/50 = 1/10

8. Probability of Overlapping Events
Event A: Roll a number less than 5
Event B: Roll an Event number
Event B
Event A
1 3 5
P (A or B) = P (A) + P (B) – P(A and B) =
4/ / / = 5/6