1. Union, Intersection

2. Intersection of Sets

3. 3 Intersection (∩) [of 2 sets]: the elements common to both sets Some guidelines when finding the intersection of 2 sets: –Usually easier to start with the set containing the least number of elements

4. 4 Solving Compound Inequalities Using Intersection Can be found in two formats: –Two linear inequalities separated by the word and –A statement containing two inequality symbols -4 < x < 7

5. Union of Sets

6. 6 Union (U) [of 2 sets]: the combination of the distinct elements from both sets Some guidelines when finding the union of 2 sets: –“Dump” the elements of both sets together and remove the duplicates

7. S T R O P 1 2 3 6 5 4 Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? P(even) = (3 evens out of 6 outcomes) (1 vowel out of 5 outcomes) P(vowel) = P(even, vowel) = Independent Events Slide 7

8. Dependent Event What happens the during the second event depends upon what happened before. In other words, the result of the second event will change because of what happened first. The probability of two dependent events, A and B, is equal to the probability of event A times the probability of event B. However, the probability of event B now depends on event A. Slide 8

9. Dependent Event Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get 2 black pens? P(black second) = (There are 13 pens left and 5 are black) P(black first) = P(black, black) = THEREFORE……………………………………………… Slide 9

10. TEST YOURSELF Are these dependent or independent events? 1.Tossing two dice and getting a 6 on both of them. 2. You have a bag of marbles: 3 blue, 5 white, and 12 red. You choose one marble out of the bag, look at it then put it back. Then you choose another marble. 3. You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back. 4. You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another tile. Slide 10

11. Find the probability P(jack, factor of 12) 1 5 5 8 x= 5 40 1 8 Independent Events Slide 11

12. Find the probability P(6, not 5) 1 6 5 6 x= 5 36 Independent Events Slide 12

13. Find the probability P(Q, Q) All the letters of the alphabet are in the bag 1 time Do not replace the letter 1 26 0 25 x= 0 650 0 Dependent Events Slide 13