Probabilities of Disjoint and Overlapping Events

1. Probabilities of Disjoint and Overlapping Events notes

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. 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 Examples: Event A 6 4 2 Event B 3 5 Event A 2 Event B 1 3 5

4. 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 Tell whether the events are disjoint or overlapping. (Hint draw Venn diagram)

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 1 2 3 Event B 5 6 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 + 3/50 = 5/50 = 1/10

8. Probability of Overlapping Events • Event A: Roll a number less than 5 • Event B: Roll an Event number 2 Event B 4 6 Event A 1 3 5 P (A or B) = P (A) + P (B) – P(A and B) = 4/6 + 3/6 - 2/6 = 5/6