 Roll a die, flip a coin  Unique 3 letter arrangements of CAT  Unique 4 digit arrangements of 1, 2, 3, 4

CP Probability & Statistics SP 2015

n! = n(n-1)(n-2)…(1) Example: 5! = 5 * 4 * 3 * 2 * 1

If event A has m outcome and event B has n outcomes then the number of possible outcomes for A or B is m + n A and B is mn

1 If you have 5 pairs of pants and 7 shirts, how many different outfits can you make? 2 6 students are running in a race. How many different race results could there be with no ties? 3How many different seating arrangement can a teacher make for a class of 30, if the classroom has 6 rows with 5 desks per row?

4 A new restaurant is offering a special: “Four Course Meal for $25”. The special allows diners to choose from 5 appetizers, 2 salads, 4 entrees and 6 desserts. Diners can choose 1 option for each course. How many different 4 course combinations are available? 5Craving ice cream? The local ice cream shop offers 24 flavors. You can get your ice cream in a sugar cone, waffle cone, cake cone or bowl. Then top it off with your choice from 8 yummy toppings. Assuming you only choose 1 flavor of ice cream and 1 topping, how many different combinations can you get?

6 How would your number of choices for question 6 change if you could also choose no toppings? 7,8 7 and 8 are different. We will come back to these 9 How many combinations can you get if you roll a dice numbered 1 – 6 and cube lettered A,B,C,D,E,F? 10How many different combinations of 5 cards can be drawn from a standard deck of 52 cards? Order does not matter, so this is different. We will come back to it.

11 How many different combinations are available if you toss a fair coin and roll a standard 6 sided die? 12How many unique sandwiches can be made using the following choices: Buns: 4 different types or no bun Patty: Chicken, Beef, Bison, Black Bean Lettuce: Romaine, Iceberg, none Tomato: Yes or no Onion: Sliced, Grilled, none Cheese: Cheddar, American, Swiss, Provolone, none

13 So you think you have this? What if for number 12 we add choices of 4 different sauces? Choosing 1 or none should be an easy calculation but what if you can choose any combination of the 4 sauces or no sauce? – this part is different (we will come back to it) 14Time to exercise: Suzy wants to go jogging. She has 5 tops, 4 pairs of shorts and 2 pairs of shoes to choose from. How many different outfits could she wear?

Number of possible arrangements when choosing r items from a set of n items and ORDER DOES NOT MATTERS

7 For question 6, how many choices would you have if you could choose 2 different flavors of ice cream and 0-8 toppings (remember you have container choices too!) 8A class wants to elect 2 officers from 10 candidates. How many different combinations can there be?

10How many different combinations of 5 cards can be drawn from a standard deck of 52 cards? Order does not matter, so this is different. We will come back to it. 13So you think you have this? What if for number 12 we add choices of 4 different sauces? What if you can choose any combination of the 4 sauces or no sauce? – this part is different (we will come back to it),

15The junior class has 4 seats to fill on student council. 950 juniors are eligible to run. How many different combinations could be chosen?

Number of possible arrangements when choosing r items from a set of n items and ORDER MATTERS

The number of distinct permutations of n objects where n 1 of the objects are identical, n 2 of the objects are identical,..., n r of the objects are identical is found by the formula:

 How many different arrangements can be made using all of the letters in  MISSISSIPPI M- 1I-4 S-4P-2

Probability allows us to go from information about random samples to information about the population.

We KNOW what outcomes COULD happen We DO NOT KNOW which outcomes WILL happen.

ExperimentOutcomes Flip a coinHeads, Tails Roll a standard die1, 2, 3, 4, 5, 6 Examples: Sample Space The collection of all possible outcomes

Probability of an event A, P(A), is a number between 0 and 1 that identifies the likelihood that event A happens. Example: Rolling a standard die P(1) = 1/6P(2) = 1/6 P(3) = 1/6P(4) = 1/6 P(5) = 1/6P(6) = 1/6

 Trial Single attempt (or realization) of a random phenomenon  Outcome The observed result of a trial  Independence (informal definition) 2 events are independent if the outcome of 1 does not influence the outcome of the other.

 Event Collection of outcomes We typically label events so we can attach probabilities to them Notation: bold capital letter: A, B, C, … Example: Roll a die and get an even E is 2,4 or 6  Sample Space The collection of all possible outcomes Example: Roll a die S = {1,2,3,4,5,6}

Observed probability gets closer to the calculated/theoretical probability

When the outcomes in a sample space are equally likely to occur then: