Communicating Quantitative Information

Spreadsheet example: credit card, Games of chance (and skill),

Party list voting and other forms of voting,Geography, GapminderHomework: Postings.

Credit card

• Unpaid balances are subject to interest!!!

• Show in Excel – Named cell– Extending patterns– More formulas (formulae?)

More on Powerball

• Chance of winning second prize: All 5 white balls and NOT the red ball– Total number of different possibilities is

combin(49,5)*42 = 80089128– 1 out of 80089128 give you the jackpot,

41/80089128 correspond to a given set of white balls but one of the other red balls!

Puzzle

• A family has 3 cars: Toyota, Ford, BMW. They park the cars in a 3 car garage, all facing forward and adjacent to one another. How many different ways are there to arrange the cars in the garage?

• Hint/suggestion: you can do this 2 ways: by formula and by enumeration (listing the ways)

New problem

• The family buys a fourth car. How many different arrangements of cars (permutations: the cars and the order matter) are there?– 4*3*2

• What if order does not matter? How many different ways?– (4*3*2) / (3*2*1) yields 4– Same question: how many ways can a car be left out

on the street? 4 ways for each of the 4 cars

Locker combinations

• 10 numbers, sequence of 3, how many?• 10 * 10 * 10

• (NOT ME, but I'm told you can pick a lock…)– try each of up to 10 numbers: HEAR A CLICK– try each of up to 10 numbers: HEAR A CLICK– try each of up to 10 numbers, pulling after each one:

Lock will open– Difficulty is 10 + 10 + 10 = 30 <<1000

Games….

• may be mixture of luck, memory, skill

• Memory/Concentration– Initial lock, but assuming perfect memory….– After you 'know' certain places, always pick a card

you don't know.

• Minesweeper– (some minesweeper programs, you cannot lose on

the first move)– still may be luck, but can use logic

• Let's try it!

Permutations from set with duplicates (multiples)

• Given A, B, C, D, E, how many different permutations of size 3– 5*4*3 5 choices for the 1st, 4 for the 2nd 3 for

the 3rd

• Given A, A, A, B, C, – (5*4*3)/(3*2*1) Need to divide by 3! = 6

because the choices of the As do not matter. Think of it as A1, A2, A3, B, C, and then saying that the choices of A's do not count.

Consider a deck of cards

• How many 5 card hands:– 52*51*50*49*48

• How many different 2 card hands– 52*51

• How many ways to draw 2 aces– 4*3

• What is probability to draw 2 aces– (4*3) / (52*51)

Extra credit opportunity

• Do research and explain source on– texas-hold-em– blackjack

• note: "counting" much less valuable when dealers use multiple decks and can shuffle whenever they want.

The game of crap(s)

• Dice game (see Guys and Dolls)• Throw 2 dice and add up numbers• 1st throw

– 7 and 11 win– 2, 3, and 12 lose– otherwise: number becomes 'the point'

• Follow-up throw– 7 loses– point wins

• Game can last any number of throws

Probabilities

• 36 possible combinations– 2: 1& 1 1/36– 3: 2&1, 1&2 2/36– 4: 2&2,1&3,3&1 3/36– 5: 2&3, 3&2,1&4,4&1 4/36– 6: 3&3,4&2,2&4,5&1,1&5 5/36– 7: 1&6,6&1,2&5,5&2,3&4,4&3 6/36– 8:– 9:– 10:– 11:– 12:

So,….

• What is the probability of winning on the first throw:– add up P of getting 7 or 11

• What is the P of losing on the first throw:– add up P of getting 2, 3, or 12

• What are the possible point values? Add up these. The last 3 numbers need to add to 1.

• For a follow-up throw: what is the P of losing (hint: P of getting a 7)

• For a follow-up throw: what is the P of winning? (hint: it depends.)

Reminder: odds versus probability

• P(event) is event/total• Odds for an event event/not_the_event

• If odds are A/B, then P(A) = A/(A+B)• If P(A) is p, then determine odds by

considering p and 1-p and multiply both numbers by factor to get whole numbers– ex. P(A) = 1/3. Then 1/3 to 2/3 translates to 1 to 2 odds

Back to craps

• What are the odds of winning on the first throw?

Party list voting

• Several years ago: Iraqi voting in the news. Party list voting is used other places:– Israel– Palestine authority– ?

• What• How• (Who)

Voting lists

• Voting lists common in several countries.• Parties decide on and publish lists (ORDERED

lists)– May be rules on lists

• no fewer (but there could be single named lists), no more• women must occupy 1/3 of first 3, 1/3 of first 6,…

• People vote for a party• After election, determine order, percentage

– Say: biggest winner is party X with 45% of vote. There are 275 seats. Then party X can send .45*275 (rounded ???) people. Move on to next party.

Compute

• 20 seats• Party A gets 50%

A1, A2, A3, etc.• Party B gets 30%

B1, B2, B3, etc.• Party C gets 10% C1, C2, C3, etc.• Party D gets 9%

D1, D2, D3, etc.• Party E gets 1% E1, E2, E3, etc.Who occupies the 20 seats?

Voting lists

• Considered more ideological…but it is the case in Iraq that many of the parties are coalitions

– Argument that 'winner take all' aka 'first past the post' can alienate large groups of voters

• Personality less important?

• Keep in mind that the Iraq election was to install a government to – write a constitution,– elect provisional assembly– elect leaders

• What do you think?

Posting opportunities

• Elections around the world

• Who elected David Cameron PM of UK?

• ???

Cumulative voting

• Another form of proportional voting gives everyone N votes to use as they wish– N different people– N for one person– some combination

• Used in small number of school board, union elections

• Used in recent voting on Portchester: posting and/or report opportunity!!!!

Old, old news

• Issue with Lani Guinier nomination– Slurred [my opinion] as being against one

man one vote, being 'quota queen'

– Guinier studied and wrote about alternative systems such as cumulative voting

• Some corporate voting is cumulative

Instance run-off

• People say / write second choice

• Iowa Presidential Caucus– If a candidate has less than 15% of people in

the room, these people go to their second choice

– Edwards issue?

Posting opportunities

• Find instances of cumulative voting

• Find instances (explain) of other way to vote

• Research (and explain the details) of a John Roberts law case involving gay rights that related to alternative type of voting

Exercise: Map drawing

Maps are mathematical objects: we will return to this subject: map projections.

• Draw map of Iraq (include border countries/bodies of water)

• Draw map of 'Mid-east': Israel, Palestine, neighboring countries, bodies of water

Extra credit posting (Use General Discussion forum): look up and comment on how well you did.)

Another fitting together puzzle

• 400 freshmen at SUNY

• 250 of these are taking a math class.

• 100 are taking neither a math class nor a science class.

• If a freshman is taking math, the probability that he/she is taking science is 40%.

• How many freshmen are taking science?

What do we know?

• 400 freshmen at SUNY• 250 of these are taking a math class.

– 150 are not taking a math class

• 100 are taking neither a math class nor a science class.– 50 students are taking science, but not math

• If a freshman is taking math, the probability that he/she is taking science is 40%.– 40% of 250 is 100 (40% is 2/5. 1/5 of 250 is 50. 2 fifths is 100)

• How many freshmen are taking science?– 50 + 100 is 150

The term probability may be misleading, but it is accurate. Of the population of freshmen taking math, if you reached down and chose one, the probability of it being someone taking science is 40%.

If time: explore gapminder

• www.gapminder.org

• Global health statistics

Homework

• Postings!!!!

• Start to think about a topic that you want to research and write about (including diagrams and charts)– more on this later