Math 2
Lesson 8-3: Independent Events
Name_______________________________
Date _____________________________
Learning Goals:
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I can define and/or identify the following: complement, independent event, dependent event.
I can illustrate the concept of independence using everyday examples of independent events.
I can predict if two events are independent, explain my reasoning, and check my statement by
calculating P(A and B) and P(A) X P(B).
I can explain and provide an example to illustrate that for two independent events, the probability of the
events occurring together are the product of the probability of each event.
Take notes and work out the examples from the video titled: Multiplication Rules for Probability
(Independent Events) https://www.youtube.com/watch?v=l_Vw-I6zYC4
Definition of Independent Events:
Examples of independent events:
Multiplication Rule #1 states: ___________________________________________
Example #1:
Example #3:
a.
b.
c.
Example #4:
Example #5:
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Examples:
I. Some physical characteristics, such as freckles, dimples, and the ability to roll one’s tongue up from the
sides, are determined in a relatively simple manner by alleles inherited from one’s parents.
A. Each person has two alleles that determine whether or not he or she will have freckles, one inherited
from the father and one from the mother. The allele for freckles is called dominant, and the allele for
no freckles is called recessive. Complete the Punnett square below to illustrate the possible
offspring for parents who each have one freckles allele and one no-freckles allele.
Mother
F  freckles
f  no freckles
Why is “freckles” represented by the capital letter?
1. Based on the Punnett square above, what is the probability that a child will not have freckles?
2. Find the probability that the couple will have a boy and the child has freckles.
3. Find the probability that the couple will have a girl and the child does not have freckles.
B. The allele for dimples is dominant and the allele for not having dimples is recessive. Suppose the
same parents from Part A have the following genotypes: The mother is homozygous for not
dimples and the father is heterozygous for dimples. Create a Punnett square illustrating the possible
offspring.
1. What is the probability that the child will have dimples?
2. Find the probability that the couple will have a girl and the child does not have dimples.
3. Find the probability that the couple will have a child that has freckles and dimples.
4. Find the probability that the couple will have a child that is a girl who has freckles but does not
have dimples.
5. Find the probability that the couple will have 3 boys who do not have freckles but do have
dimples.
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II. Suppose Ralph is playing a game in which he needs to roll a pair of dice and get doubles and then
immediately roll the dice again and get a sum of six. He wants to know the probability that this will
happen.
A. Which of the following best describes the probability Ralph wants to find?
Option 1: P(gets doubles on the first roll or gets a sum of six on the second roll)
Option 2: P(gets doubles on the first roll and gets a sum of six on the second roll)
Option 3: P(gets doubles and a sum of six)
B. What is the probability?
III. For each of the following questions, explain whether it is reasonable to assume that the events are
independent. Then, if it applies, use the Multiplication Rule to answer the question.
A. What is the probability that a sequence of seven flips of a fair coin turns out to be exactly
HTHTTHH?
B. What is the probability that a sequence of seven flips of a fair coin turns out to be exactly
TTTTTTH?
C. According to the National Center for Education Statistics, 27.9% of public school students live in a
small town or rural area. If you select 5 students at random, what is the probability that they all live
in a small town or rural area?
D. According to the National Center for Education Statistics, the percentage of students who are
homeschooled in the United States is 2.2%. If you pick 10 students at random in the United States,
what is the probability that none of the 10 are homeschooled?
E. Refer to Part d. You pick a family with two school-age children at random in the United States.
What is the probability that both children are homeschooled?
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IV.
ANSWERS:
V. According to the National Safety Council, many drivers frequently do not use seat belts when they
drive. In recent years, however, seat-belt use has been gradually increasing. It is estimated that the
probability that a driver uses a seat belt is 0.68. Find the probability that three randomly selected drivers
passing a particular check point will be using their seat belts.