Combination and Permutations Quiz! Please take out a piece of notebook paper. For each question state if it is a permutation, combination or counting principle AND solve!

You have five new books to read You have five new books to read. You want to take two of them with you on vacation. In how many ways can you choose two books to take? Suppose that first, second and third-place winners of a contest are to be selected from eight students who entered. In how many ways can the winners be chosen? Pens are available in three colors, and four tips. How many different choices of pens you have? A code is being created and contains 5 characters. The first three are letters and the last two are digits. How many possibilities are there for codes if letters and digits cannot be repeated? What is the difference between a permutation and combination?

Probability

Probability An experiment is a process, such as rolling a dice or tossing a coin, that gives results called outcomes. The sample space ,S , of an experiment is the set of all possible outcomes Ex: Tossing a coin S={H,T} An event is any subset of the sample space of an experiment

Sample Space Example If we toss a coin three times and record the results in order, what is the sample space? S={HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} What is the event of exactly two heads? S={HHT, HTH, THH} What is the event of at least two heads? S={HHH, HHT, HTH, THH}

Probability If S is the sample space of an experiment and E an event. The probability of E is Probabilities should ALWAYS be between 0 and 1 If P(E)=1 then it is a certain event If P(E)=0 then it is an impossible event

Finding Probability Example A coin is tossed three times. What is the probability of getting exactly two heads? At least 2 heads? No heads?

Probability Example 2 A five card hand is drawn from a standard deck of 52 cards. What is the probability that all five cards are spades?

Probability Example 3 A bag containing 20 tennis balls, of which 4 are defective. If two balls are selected at random from the bag, what is the probability that both are defective?

Complement of an event The complement of an event ,E , is the set of outcomes in the sample space that are NOT in E.

Example An bag contains 10 red balls and 15 white balls. Six are drawn at random from the bag. What is the probability at least one is red?

Mutually Exclusive Events Two events with no outcomes in common are mutually exclusive. Example: in drawing a card from a deck, the events E: the card is a queen, and F: the card is an ace are mutually exclusive

Mutually Exclusive Example A card is drawn from a standard deck. What is the probability that the card is either a seven or a face card? Two events: E: the card is a 7 F: the card is a face card

Probability of the Union of 2 events If two events are not mutually exclusive then they share outcomes

Example What is the probability that a card drawn from a standard 52 card deck is either a face card or a spade? Events: E: the card is a face card F: the card is a spade

Probability of Independent Events This is used when we want to find the probability of an event AND another event. Independent means the probability of the first event does not effect the probability of the second event Ex: tossing a fair coin

Example A jar contains 5 pink marbles and 4 green marbles. A marble is drawn at random from the jar and replaced, then another marble is drawn. What is the probability both marbles are pink?

Standard Deck of Cards 4 suits (13 of each) Diamonds (Red) Hearts (Red) Spades (Black) Clubs (Black) Face Cards (one of each in every suit) King Queen Jack