TOPIC ACTIVITY 3 HABITS OF MIND Categorizing Scenarios . Reason abstractly and quantitatively. . Construct viable arguments and Involving Events critique the reasoning of others. In this activity, you will learn how to describe events as a subset of a sample space. A set is a collection of items. If x is a member of set B, then x is an element of set B. Consider the examples of disjoint sets, intersecting sets, and the union of sets. WORKED EXAMPLE TAKE NOTE... Disjoint Sets N Two or more sets Let / represent the set of even are disjoint sets integers. Let 7 represent the set when they do not AN have any common of odd integers. elements. Two The set of even integers and the or more sets are set of odd integers are disjoint intersecting sets because the two sets do not share any common elements. when they do have An integer cannot be both odd common elements The union of sets and even. is a set formed by Intersecting Sets combining all the V M Let V represent the set of palb soul members of the multiples of 2. Let M represent the 10 5 sets. The set lists a set of multiples of 5. O AN 20 15 member only once The set of multiples of 2 and 30 25 the set of multiples of 5 are intersecting because they share at least one common element: 10, 20, 30, and so on. buie bris lubege oxsif mon esbage lemne wey isbigers ?) The Union of Sets endl to vos balls osie o unlac Let B represent the set of positive B C integers. Let C represent the set of negative integers. The union ring. Inc. W N - WNL of these two sets is the set of integers (except for 0). 1 Consider the letters in the words crafty and crate. a What set do you form by taking the intersection of the letters in the two words? What set do you form by taking the union of the letters in the two words?Independent events a Which the occurrence of one event has no impact on the occurrence of the other event. Dependent events are events for which the occurrence of one event impacts the occurrence of subsequent events. consider the examples of independent events and dependent events. WORKED EXAMPLE A jar contains 1 blue marble, 1 green marble, and 2 yellow marbles. TOPIC 1 Independent Events Imagine that you randomly choose a yellow marble, replace the marble in the jar, and then You can see this visually randomly choose a yellow marble again. using a tree diagram. The event of choosing a yellow marble first does not affect the event of choosing a yellow marble second because the yellow marble chosen first is replaced in the jar. BG Y Y B G Y Y B G Y Y B G Y Y The events of randomly choosing a yellow marble first and randomly choosing a yellow marble second are independent events because the first yellow marble was replaced in the jar. WORKED EXAMPLE A jar contains 1 blue marble, 1 green marble, and 2 yellow marbles. Dependent Events You can see this visually Imagine that you randomly choose a yellow using a tree diagram. marble, and then without replacing the marble in the jar, randomly choose a yellow marble again. The event of choosing a yellow marble first does affect the event of choosing a yellow BGY BGY marble second because the yellow marble GYY BYY chosen first is not replaced in the jar. The events of randomly choosing a yellow marble first and randomly choosing a yellow marble second are dependent events because the jar . the first yellow marble was not replaced in