UNDERSTANDING INDEPENDENT EVENTS Adapted from Walch
Education
Slide 3
Key Concepts 7.1.3: Understanding Independent Events 2 Two
events A and B are independent if and only if they satisfy the
following test: P(A and B) = P(A) P(B) Using set notation,
Slide 4
Concepts, continued. 7.1.3: Understanding Independent Events 3
In a uniform probability model, all the outcomes of an experiment
are assumed to be equally likely, and the probability of an event
E, denoted P(E), is given by
Slide 5
Concepts, continued. 7.1.3: Understanding Independent Events 4
The relative frequency of an event is the number of times it occurs
divided by the number of times the experiment is performed (called
trials) or the number of observations:
Slide 6
Note: 7.1.3: Understanding Independent Events 5 When relative
frequency is used to estimate the relevant probabilities, then the
definition of independent events can be used to determine whether
two events seem to be dependent or independent, based on the
data.
Slide 7
Probability and relative frequency are related as follows:
7.1.3: Understanding Independent Events 6 The probability of an
event can be used to predict its relative frequency if the
experiment is performed a large number of times Relative frequency
can be used to predict the probability of an event. In general, as
the number of trials or observations increases, the prediction
becomes stronger
Slide 8
The Addition Rule 7.1.3: Understanding Independent Events 7
Remember: If A and B are any two events, then the probability of A
or B, denoted P(A or B), is given by P(A or B) = P(A) + P(B) P(A
and B). Using set notation, the rule is
Slide 9
Practice 7.1.3: Understanding Independent Events 8 Trevor
tosses a coin 3 times. Consider the following events. For each of
the following pairs of events, determine if the events are
independent.
Slide 10
Step 1 7.1.3: Understanding Independent Events 9 List the
sample space. Sample space = {HHH, HHT, HTH, HTT, THH, THT, TTH,
TTT}
Slide 11
Step 2 7.1.3: Understanding Independent Events 10 Use the
sample space to determine the relevant probabilities. There are 4
outcomes with heads first. There are 4 outcomes with heads second.
There are 2 outcomes with exactly 2 consecutive heads.
Slide 12
Step 2, continued 7.1.3: Understanding Independent Events 11
There are 2 outcomes with heads first and heads second. There is 1
outcome with heads first and exactly 2 consecutive heads. There are
2 outcomes with heads second and exactly 2 consecutive heads.
Slide 13
Step 3 7.1.3: Understanding Independent Events 12 Use the
definition of independence to determine if the events are
independent in each specified pair. A and B are independent.
Slide 14
Conclusion 7.1.3: Understanding Independent Events 13 A and C
are independent. B and C are dependent.
Slide 15
Try this problem: 7.1.3: Understanding Independent Events 14
Landen owns a delicatessen. He collected data on sales of his most
popular sandwiches for one week and recorded it in the table below.
continued Bread choice Sandwich choice Landens club Turkey melt
Roasted chicken Veggie delight Country white4425 8 Whole
wheat24282634 Sourdough24272431
Slide 16
7.1.3: Understanding Independent Events 15 Each of the
following statements describes a pair of events. For each
statement, determine if the events seem to be independent based on
the data in the table. A random customer orders Landens club
sandwich on country white bread. A random customer orders the
roasted chicken sandwich on whole wheat bread.