Illustrates events, and union and intersection of events.pptx

for math 10 learners

1. Illustrates Events, Union and Intersection of Events

2. Objectives: Illustrate events, and union and intersection of events Determine the union and intersection of events Use Venn Diagram in illustrating the union and intersection of events

3. Let’s Review: What are these symbols?   2.   3. { },   Union Intersection Null set or empty set

4. Let’s Review: What about this? Venn Diagram

5. R E P I T X N M E S E E X P E R I M E N T S

6. Experiments are activities like tossing of coins, rolling of dice, picking a card from a deck of cards or randomly choosing a ball from a box which could be repeated over and over again, and which have well-defined results.

7. M E O C T U O S O U T C O M E S

8. Outcomes possible results of the experiment Example : Roll a die- outcomes are the 1,2, 3,4,5,6

9. A P C E M S L A E S P S A M P L E S P A C E

10. Sample Space the set of all possible outcomes of an experiment denoted by S. Example: From the experiment “Rolling a die” S = {1, 2, 3, 4, 5, 6} From the experiment “Tossing a coin” S = {H, T}

11. Directions: For the given experiment, write the outcomes and the sample space. 1. Three coins are tossed HHH, HHT, HTH, HTT, THH, THT, TTH, TTT Outcomes: Sample Space: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

12. E T S S E T S S

13. Sets are the collections of items and using the bracket { } it may contain numbers, days of the week, or names of friends {A, B, C, D, E}

14. Sets are the collections of items and using the bracket { } it may contain numbers, days of the week, or names of friends {1, 2, 3, 4, 5}

15. E N E T M E L S E L E M E N T S

16. Elements the items contained within a set that satisfies the criteria

17. E N T V E E V E N T

18. Event a subset of a sample space a specific or collection of outcomes Simple Events Any event which consists of a single outcome in the sample space Compound Events event which consists of more than one outcome

19. Illustrative Examples:

20. Compound Events

21. Union the blending of both sets (indicates “or”) special symbol   Intersection when the two sets overlap (indicates “and”) special symbol  

22. Union of Events Consists of elements belonging to event A, event B, or both A and B this is written as A or B     A B

23. Intersection of Events events are occurring together this is written as A and B   consists of all elements in event A and B at the same time   A B

24. Given the following sets:     Then illustrate using Venn Diagram Find:    

25. Given the following sets:     (A) (B) 6 2 7 4 8 12 11 10 Diagram Find:   answer:  

26. Given the following sets:     (A) (B) 7 4 8 12 11 10 Diagram Find:     2 6 answer:  

27. Example 1: If Event and   Event     or empty set  

28. Example 2 If Event A is letters from the word MARBLE and Event B all the VOWELS Given: Event A = {M, A, R, B, L, E} Event B = {A, E, I, O, U}    

29. Example 3 (A) (B) 2 3 5 6 1 9 10 4 8 7 Given: Event A ={1,2,3,5,6,9} Event B ={2,3,4,5,7,8,10}   Find  

30. Example 3 (A) (B) 2 3 5 6 1 9 10 4 8 7 Given: Event A ={1,2,3,5,6,9} Event B ={2,3,4,5,7,8,10}  

31. Example 3 (A) (B) 2 3 5 6 1 9 10 4 8 7 Given: Event A ={1,2,3,5,6,9} Event B ={2,3,4,5,7,8,10}   Find   2 3 5

32. Exercises Directions: A spinning wheel is divided into 12 equal sectors and numbered 1-12. The following events were listed. Find the following: = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {1, 3, 5, 7, 9, 11} C = {2, 3, 5, 11} E = {1, 4, 9} B = { 2, 4, 6, 8, 10, 12} D = {1, 2, 3, 4, 5, 6} F = {1, 8}   5.  

33. Complement of an Event the set of all outcomes that are NOT in the event Example S = {1,2,3,4,5,6} A = {1,2,3} The complement of an event (A’) is read as “A complement” meaning event A does not occur. So, the event A’ is the set consisting all the outcomes in the sample space S that are not in A. A’ = {4, 5, 6}   A 1 3 2 4 5 6 the shaded region in the Venn diagram at the right shows the A’

34. Example S ={1,2,3,4,5,6} A = {1,2,3} B = {2,4,6}     A B 2 1 3 4 6 5 A’ = {4, 5, 6} A B 2 1 3 4 6 5   B’ = {1, 3, 5} Find A’ and B’

35. Mutually Exclusive Events events that cannot occur at the same time events that have no common element A B There is no intersection between events A and B

36. Not Mutually Exclusive Events events that intersect or there are outcomes that are common to them. events that may occur at the same time A B There is an intersection between events A and B

37. Direction: The following events were listed, find the following. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 3, 5, 7, 9} B = {3, 4, 5, 6, 8, 10} C = {2, 4, 6, 8, 10}

38. Directions: Write the sample space (S) for each experiment. ___________________ 1. Tossing of two coins ___________________ 2. Rolling a pair of dice Practice Exercise