Probabilities of Compound Events Download

Transcript
Lesson 10.4 Probability of Disjoint and Overlapping Events
Learning Goal: (S-CP.A.1 and S-CP.B.7)
I can use the Addition Rule to find probabilities of disjoint (mutually exclusive) and overlapping
events.
Essential Question: How can you find probabilities of disjoint mutually exclusive and
overlapping events?
Homework Discussion
c. 89%
d. not ind
c. 21%
d. ind
Exploration
A six-sided die is rolled. Draw a Venn Diagram that relates the two events.
Venn Diagram
1. Event A: The result is an even
number.
Event B: The result is a prime
number.
Are the events disjoint or overlapping?
P(A) =
P(B) =
P(A and B) =
P(A or B) =
P(A ∩ B)
P(A U B)
Venn Diagram
2. Event A: The result is 2 or 4.
Event B: The result is an odd
number.
Are the events disjoint or overlapping?
P(A) =
P(B) =
P(A and B) =
P(A or B) =
P(A ∩ B)
P(A U B)
In general, if event A and event B are disjoint, then what is the probability that event A or
event B will occur?
In general, if event A and event B are overlapping, then what is the probability that event A or
event B will occur?
Probabilities of Compound Events
Compound Events: the union or intersection of two events
Disjoint (Mutually Exclusive) Events: no outcomes in common
Overlapping Events: one or more outcomes in common
Match the word to the diagram that it represents
Union
Intersection
Disjoint
Union
Intersection
Disjoint
Overlapping
Overlapping
Probabilities of Compound Events
P(A or B) = P(A) + P(B) - P(A and B)
If the two events are disjoint (mutually exclusive) then:
P(A or B) = P(A) + P(B)
Why?
Example:
A card is randomly selected from a standard deck of 52 playing cards. What is the
probability that it is a 10 or a face card?
Step 1: Disjoint or Overlapping?
4 suits (2 red, 2 black)
Why?
Step 2: Determine the events.
Event A: card is a 10
Event B: face card
13 cards per
suit
3 face cards per
suit
Step 3: Find the probabilities.
P(A) =
P(B) =
P(A or B) =
Example 2:
A bag contains cards numbered 1 through 20. One card is randomly selected. What is
the probability that the number on the card is a multiple of 3 or a multiple of 4?
Step 1:
Step 3:
Step 2:
Group Consensus
Even Groups:
A card is randomly selected from a standard deck of 52 playing cards. What is the
probability that it is a face card or a spade?
Odd Groups:
Two six-sided dice are rolled. What is the probability that the sum of the numbers
rolled is a multiple of 4 or is 5?
Example 3:
Out of 200 students in a senior class, 113 students are either varsity athletes or on the
honor roll. There are 74 seniors who are varsity athletes and 51 seniors who are on the
honor roll. What is the probability that a randomly selected senior is both a varsity athlete
and on the honor roll?
Step 1: Disjoint or Overlapping
Step 2: Determine Events
Event A:
Step 3: Find the Probabilities
P(A) =
P(A and B) =
P(B) =
Event B:
P(A or B) =
Exit Problem:
Practice to Strengthen Understanding
Hmwk # 19 BI p567 #1-15