Probabilities of Disjoint and Overlapping Events notes

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.

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 2 Event B Event A Event B 3 5

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 8 th grader. Event B: Select a boy

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 5 6 4

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

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

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