9D Compound Events, 9E Tree Diagrams, 9F Sampling with and without Replacement Unit 1: Probability 9D, 9E, 9F 4/6/2019 8:18 AM

Sampling process of selecting an object from a large group of objects and inspecting it with replacement: put back without replacement: put to the side When might each form of sampling be useful? food samples at grocery store bingo quality control statistics 9D, 9E, 9F 4/6/2019 8:18 AM

Fundamental Counting Principle Copy used to determine the size of the sample space for an event or a set of combined events For each of the following, how many are possible? rolling two normal dice and flipping a coin 4-digit debit card pin numbers 4-digit debit card pin numbers (no repetition of any digit) ways to arrange 5 textbooks on a shelf phone numbers within one area code ways to stack a deck of cards 9D, 9E, 9F 4/6/2019 8:18 AM

Compound Events Box X contains 2 blue and 2 green balls and Box Y contains 3 red and 1 white ball. A ball is randomly selected from each of the boxes. Determine the probability of getting “a blue ball from X and a red ball from Y.” P(B from X and R from Y) = 9D, 9E, 9F 4/6/2019 8:18 AM

Independent Events If A and B are two independent events, where the occurrence of one of them does not affect the occurrence of the other, then P(A and B) = P(A) · P(B) Are the compound events in the previous box example independent? Yes, the choice from one box does not impact the choice from the other. A coin is tossed, a die is rolled, and a card is chosen simultaneously. P(head and 3 and king) Copy Copy 9D, 9E, 9F 4/6/2019 8:18 AM

Dependent Events Two or more events are dependent if they are not independent. P(A then B) = P(A) · P(B given that A has occurred) P(A then B) = P(A) · P(B | A) A box contains 4 blue and 2 gold lanyards. Two lanyards are randomly selected, one by one from the box, without replacement. Using the rule and a tree diagram, find: P(both are blue) P(the first is blue and the second is gold) P(one is blue and the other is gold) Copy Copy 9D, 9E, 9F 4/6/2019 8:18 AM

Tree Diagrams A box contains 4 blue and 2 gold lanyards. Two lanyards are randomly selected, one by one from the box, once without replacement and once with replacement. Create two tree diagrams to represent the separate cases. When using tree diagrams to determine probability: The probability of each branch is calculated by multiplying the probabilities along that path. If two or more branch paths meet the description of the compound event, the probability of each path is found and then added together. For each scenario, find P(GG) Compare the “conditional probability” and “independent events” formulas in the formula booklet. Which of the two would technically work in all cases and encapsulate the other? 9D, 9E, 9F 4/6/2019 8:18 AM

Guided Practice p. 273: 1,3,4,5 p. 274: 1,2,5 p. 277: 2,5,6 p. 279: 2,4,5,7 Read and follow all instructions. List the page and problem numbers alongside your work and answers in your notes. Use the back of the book to check your answers. Copy 9D, 9E, 9F 4/6/2019 8:18 AM