Download Exam 3 Review

Math 101 – Exam 3 Review (Chapters 2 and 3 - concepts from 2.1 are listed but will be less
emphasized, since they were covered on Exam 2)
Historical Figures (* are most important)
*John Venn (again)
*Augustus DeMorgan
*Blaise Pascal
*Pierre de Fermat
*Gregor Mendel
*Reginald Punnett
*Nancy Wexler
Christian Kramp
Antoine Gombauld
Math Concepts
 Sets and their properties
o Empty sets, the Universal set, and mutually exclusive sets
o Union and Intersection
o Cardinal Number formula (related to union and intersection)
o The Complement of a Set
 Venn Diagram Shading
 Blood Types
 DeMorgan’s Law for simplifying complements
 2-circle and 3-circle Venn Diagrams – cardinal numbers of subsets and probability
calculations
 Combinatorics – 3 main problem types:
o Counting principles for independent events
o Permutations
o Combinations
 Factorial notation, and reducing factorial fractions
 Distinguishable permutations
 Probability vocabulary
o experiments
o outcomes
o sample space
o event
o odds - true odds vs. house odds
o Probability (aka theoretical probability) vs. relative frequency (aka experimental
probability)
 Coin flipping calculations – sample space, probabilities of events
 Law of large numbers
 Mendel’s laws of genetics (dominant and recessive genes)
 Punnett Squares
 Inherited diseases:
o Cystic Fibrosis & Tay Sachs (recessive)
o Sickle Cell Anemia (co-dominant)
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o Huntington’s (dominant)
Range of possible probabilities; probabilities of certain and impossible events
Mutually Exclusive events and their probabilities
Roulette (if a problem of this type is given, a chart of the house odds will be provided)
Pair of Dice calculations - sample space, probabilities of events
Complements in probability calculations (e.g., the paintball problem, the birthday
problem).
Probabilities in Card Hands
Lottery Calculations
Expected Value of experiments
o games - roulette, lottery, Keno, cards
o other “risk-value” problems, like insurance
Decision Theory - statistical and psychological factors
Applications - There are many applications scattered throughout the math concepts,
including genetics, diseases, roulette, lotteries, insurance
Practice Problems
1. How many 3-digit house numbers can be formed from the digits 1, 2, 3, 4, 5, 6, 7 if the
first digit must be 1, but replacement is allowed (digits may be reused)?
2. a) Find the value: 12 P3
b) Find the value and simplify:
x P1
3. For a standard deck of cards with no jokers,
Let event Q = “drawing a queen”, event R = “drawing a red card”
a) Find p(Q  R)
b) Find o(Q)
4. The gene for Tay-Sachs disease (t) is recessive, and (N) represents a normal gene. If 2
parents have genotypes types NN and Nt:
a) What is the probability that their child will have Tay-Sachs disease?
b) What is the probability that their child will be a carrier?
c) What is the probability that their child will neither have the disease, nor be a carrier?
5. The probabilities of amounts a customer will spend on a pair of shoes are shown below.
What is the expected value of the amount that a customer will spend on shoes?
Amount
Probability
0
0.3
$30
0.4
$50
0.2
$80
0.1
6. At a DMV (Dept. of Motor Vehicles office), the following probabilities are observed:
Prob. of passing the written test on the first try: 0.45
Prob. of passing the road test on the first try: 0.35
Prob. of passing at least one test on the first try: 0.7
a) Find the probability of failing both tests on the first try
b) Find the probability of passing both tests on the first try
7. Of 40 students surveyed, the # of students who completed each class is listed:
19
25
26
5
16
6
2
a)
b)
c)
d)
Art
Music
PE (Physical Education)
completed all 3
Music and PE
Music only
Art only
Fill in the Venn diagram showing appropriate numbers for each subset.
How many respondents did not complete any of the 3 classes?
What percent of all students took Music?
What percent of all students took Art or PE?