Addition Rule/Mutually Exclusive and Non-Mutually Exclusive Events
Fundamental Counting Principle and the Complement Rule
Multiplication Rule and Independent/Dependent Events
Venn Diagrams
Two-Way Tables
100
Is the following event mutually exclusive or non-mutually exclusive?
P(choosing a Queen or diamond from a standard deck of cards)
non-mutually exclusive
(there is overlap: queen of diamonds)
100
What is the complementary event of "at least one"?
none
100
What does the notation P(B|A) represent?
P(B|A) means the probability of event B, given that event A already occurred
100
A group of students were surveyed to see who does hockey and who does gymnastics. The results are displayed in the following Venn Diagram. What does the shaded region in the following Venn Diagram represent?
the shaded region represents those who do both hockey and gymnastics
(6 people)
100
Fill in the blanks in the following two-way table.
check students' answers
200
What is the difference between the addition rule formula for mutually exclusive events and the addition rule formula for non-mutually exclusive events?
Write the formula for each and label appropriately to show your answer.
addition rule for mutually exclusive events:
P(A or B) = P(A) + P(B)
addition rule for non-mutually exclusive events:
P(A or B) = P(A) + P(B) -P(A and B)
200
Find the total number of possible outcomes for the following scenario.
You spin a spinner with the colors red, orange, yellow, green, blue, and violet two times.
total number of outcomes: 36
6 outcomes: event 1
6 outcomes: event 2
(6)(6) = 36 = 6^2 outcomes!
200
What is the multiplication rule for independent events? What is the general multiplication rule, which can be used for dependent events?
multiplication rule for independent events: P(A and B) = P(A) x P(B)
general multiplication rule: P(A and B) = P(A) x P(B|A)
200
Make a Venn Diagram from the following two-way table.
answers will vary- check students' work!
200
Daily Double!
Make a two-way table from the following Venn Diagram:
DAILY DOUBLE
Check students' work!
300
Find the following probabilities. Write your answer for all of parts a-c. Think of a standard, 52-card deck of cards. You are choosing one card.
a) P(choosing a club or spade)
b) P(choosing a face card or a diamond)
c) P(choosing a red card or choosing a jack)
a) P(choosing a club or spade) = (13/52) + (13/52) = 26/52 = 1/2 = 50%
b) P(choosing a face card or a diamond) = (12/52) + (13/52) - (3/52) = 22/52 = 42.3%
c) P(choosing a red card or jack) = (26/52) + (4/52) - (2/52) = 28/52 = 53.8%
300
On a pop quiz in history containing 5 multiple choice questions with 4 possibilities for each, you randomly guess each answer. Find the probability that you get at least one answer correct.
P(at least one correct) = 1 - P(none correct)
P(none correct) = P(all wrong)
P(all 5 wrong) = (3/4)^5 = 0.2373
1- 0.237 = 0.763 = 76.3% chance that you get at least one correct.
300
What is the difference between independent and dependent events? Explain fully.
Events are independent if the outcome of one event does not impact the outcome of the other event(s).
Events are dependent if the outcome of one event does impact the outcome of the other event(s).
300
Given that a randomly selected individual does not have a college degree, what is the probability that they listen to audiobooks?
P(no college degree) = 90 + 510 = 600
P(listen to audiobooks |no college degree) = 90/600 = 0.15 = 15%
300
Use the following two way table to answer the following question.
Explain why P(driver's license or car) does not equal P(driver's license) + P(car). Then, find P(driver's license or car).
P(driver's license or car) does not equal P(driver's license) + P(car) since the events of has driver's license and has car are not mutually exclusive. Since there is an overlap between the two, you need to subtract that off from the sum.
P(driver's license or car) = P(driver's license) + P(car) - P(driver's license and car)
= (67/100) + (47/100) - (43/100) = 71/100= 71%
400
Identify and correct the error from the following student work sample.
Q: Find P(Sophomore or biology)
P(sophomore or biology) = (199/360) + (160/360) = 359/360= 0.997 = 99.7%
the events sophomores and biology are not mutually exclusive! thus, you need to subtract off P(sophomores and biology) at the end!
Correct work:
P(sophomore or biology) = (199/360) + (160/360) - (144/360) = 215/360 = 0.5972 = 59.7%
400
You go to Dunkin and are trying to decide what to order. There are 4 donut options: jelly, chocolate, glazed, and frosted. There are 3 drink choices to choose from: iced tea, iced coffee, and a refresher. How many different breakfast combinations (consisting of one donut and one beverage are there to choose from)? List out all of the possible combinations.
12 possible options
(make a tree diagram)
iced tea: jelly, chocolate, glazed, frosted
iced coffee: jelly, chocolate, glazed, frosted
refresher: jelly, chocolate, glazed, frosted
400
At a large university, the probability that a student is on the Dean’s list and takes calculus is 0.042. The probability that a student is on the Dean’s list is 0.21. Find the probability that a student takes calculus, given that he or she is on the Dean’s list.
P(calculus|Dean's list) = 0.2 = 20%
400
Daily Double!
What percentage of students do not do a club and do not do a sport?
A recent survey at a high school revealed that 45% of its students do a sport, 35% do a club, and 15% do both a club and a sport.
35%
(Make a Venn Diagram or 2-way table to help you!)
400
Create a two-way table from the following information.
A 2018 survey of 150 U.S. teenagers showed that 86% of U.S. teenagers use Snapchat, 32% use Instagram, and 18% use both.
Then, answer the following:
a) How many U.S. teenagers use snapchat but not Instagram?
b) How many U.S. teenagers do not use snapchat nor Instagram?
c) Given that a teenager uses Instagram, what is the probability that they use snapchat?
*Tables will vary; can do with percents or numbers themselves!
a) 102 teenagers
b) 0
c) 27/48 = 0.5625 = 56.25%