Notes 5.2: Basic Probability Concepts
Learning Target Basic Probability Concepts? I can list a sample space and assign probabilities to each outcome?Sample Space: Lists all possible outcomes; denoted: S = {outcomes usually listed in brackets}Example 1: List the sample space for rolling a single die. S = {}Note: The fundamental counting principle and tree diagrams are often used to determine sample spaces.Example 2: A coin is flipped 3 times. Find the sample space.Step 1: List possible results from 1st flipStep 2: Extend branches from each possibility in the 1st flip to possibilities of 2nd flipStep 3: Extend branches from each possibility in the 2nd flip to possibilities for the 3rd flip(Hint: In the tree diagram, each set of branches = one flip or coin.)HTSample space of 3 coins = { }Example 3: Find the sample space for gender in a family with 2 children.Sample space of 2 children = {}Example 4: Two dice are rolled and the sum is recorded. Find the sample space. Hint: A tree diagram could be used, but it would take a while. With only 2 outcomes, a chart will be easier!123456123456Once you know your sample space, you can determine probabilities.171450043180P(Event) = Number of times event occursTotal number of outcomesP(Event) = Number of times event occursTotal number of outcomesExample 5: In a single coin toss, find P(H)Example 6: When tossing a pair of dice, find P(Sum = 5) Example 7: In a standard deck of cards, find P(Ace)Example 8: In a family with 2 children, find P(2 boys) or P(BB)? I can classify events as independent or dependent?Independent Events: If one event occurs, it does not affect the probability of the other event occurring.Dependent Events: If one event occurs, it does affect the probability of the other event occurring. Example 9: Determine whether the following events are independent or dependent.Rolling a 6 on a die and then tossing a coin and getting a TDrawing a red card out of a standard deck of cards and then draw a black card without replacing the red card.Drawing a red card out of a standard deck of cards and then draw a black card after replacing the red card (and reshuffling).You select a game piece for monopoly and then someone else selects a game piece.? I can classify events that are disjoint (mutually exclusive) or joint (not mutually exclusive) ?Disjoint or Mutually Exclusive Events: Events that cannot occur at the same time. Joint or Not Mutually Exclusive Events: Events that can occur at the same time.Example 10: Determine whether the following events are disjoint (mutually exclusive) or joint (not mutually exclusive). Drawing one card and getting a queen and a king from a standard deck of cardsDrawing one card and getting a black card and a jack from a standard deck of cardsRolling a pair of dice and getting a sum of 5 and a sum of 7 Rolling a pair of dice and getting a sum of 10 and doubles Tossing a coin and getting a H and a T ? I can create a probability model by listing outcomes and their probabilities ?Probability Model: lists the sample space and assigns probabilities to each outcome (easy to put in a table)Example 11: Create a probability model of rolling a die and then use the probability model to determine probabilities of certain events occurring.Outcome123456ProbabilityP(Even) = _____P (Greater than 3) = _____P (Even and Greater than 3) = ______Example 12: Create a probability model for the outcomes of tossing 2 coins and then use the probability model to determine the probabilities of certain events occurring.P( HH) = ______P (HT or TH) = ______P (HH or TT) = ________P (HH and TT) = ____ ................
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