# 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
• 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

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:

b) Find the value and simplify:

1. 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)

1. 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?

1. 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
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

1. 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?