# Historical Figures (* Are Most Important)

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
- Empty sets, the Universal set, and mutually exclusive sets
- Union and Intersection
- Cardinal Number formula (related to union and intersection)
- 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:
- Counting principles for independent events
- Permutations
- Combinations
- Factorial notation, and reducing factorial fractions
- Distinguishable permutations
- Probability vocabulary
- experiments
- outcomes
- sample space
- event
- odds - true odds vs. house odds
- 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:
- Cystic Fibrosis & Tay Sachs (recessive)
- Sickle Cell Anemia (co-dominant)
- 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
- games - roulette, lottery, Keno, cards
- 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

- 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)?
- a) Find the value:

b) Find the value and simplify:

- For a standard deck of cards with no jokers,

Let event Q = “drawing a queen”, event R = “drawing a red card”

a) Find

b) Find o(Q)

- 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?

- 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

- 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

- Of 40 students surveyed, the # of students who completed each class is listed:

19 Art

25 Music

26 PE (Physical Education)

5 completed all 3

16 Music and PE

6 Music only

2 Art only /

a) Fill in the Venn diagram showing appropriate numbers for each subset.

b) How many respondents did not complete any of the 3 classes?

c) What percent of all students took Music?

d) What percent of all students took Art or PE?