Mutually and Not Mutually Exclusive Events

Mutually and Not Mutually Exclusive events

1. Number cards 1 through 30 are shuffled and placed on the table face down. One card is chosen at random. What is the probability that the number chosen is:

2. a multiple of 3 or a multiple of 4? A = {3, 6, 9 , 12, 15, 18, 21, 24, 27, 30} = 10 B = {4, 8, 12, 16, 20, 24, 28} P(AUB) = (10 + 7) – 2 = 15/30 = 1/2

3. a multiple of 3 and a multiple of 4? A = {3, 6, 9 , 12, 15, 18, 21, 24, 27, 30} = 10 B = {4, 8, 12, 16, 20, 24, 28} P(A B) = 2/30 = 1/15  

4. an even number or an odd number? A = {2, 4 , 6, 8 ,10, 12, 14, 16, 18, 20 ,22, 24, 26, 28, 30} = 15 B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,25, 27,29} = 15 P(A U B) = 15 + 15 = 30/30 = 1

5. an even number and an odd number? A = {2, 4 , 6, 8 ,10, 12, 14, 16, 18, 20 ,22, 24, 26, 28, 30} = 15 B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,25, 27,29} = 15 P(A B) = 0  

6. a multiple of 5 or contains the digit 2? A = {5, 10, 15, 20, 25, 30} = 6 B = {2, 12, 20, 21,22, 23,24, 25,26, 27,28, 29} = 12 P(A B) = (6 + 12) - 2 = 16/30 = 8/15  

7. a multiple of 3 and contains the digit 2? A = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30} = 10 B = {2, 12, 20, 21,22, 23,24, 25,26, 27,28, 29} = 12 P(A B) = 4/30 = 2/15  

8. Working by Group Each group will be given whiteboard and worksheet to work on, each group will answer the following questions and will be given points. The group with the highest score combine with the worksheet will be declared winner.

9. For items #1 & 2. In an experiment of tossing a six – sided die once, let A be the event of getting a factor of 6 and B be the event of getting an odd number.

10. 1. What is A ∪ B? Answer . (A U B) = {1, 2, 3, 5, 6} A = {1, 2, 3, 6} B = {1, 3, 5}

11. 2. What is the cardinality of A ∩ B? Answer . 2 {1, 3}

12. 3. A box contains 7 black marbles, 8 white marbles, and 5 yellow marbles. If a marble is drawn at random, what is the probability of getting a black or a yellow marble? Answer . 3 / 5 P(B U Y) = (7+5)/20=12/20=3/5

13. 4. A letter is randomly chosen from the word “MATHEMATICS”. Find the probability that a letter A or T is selected. Answer . 4/11 P(A U T) = (2+2)/11=4/11

14. 5. A die is rolled once. What is the probability that the result is an even number or a factor of 2? Answer . 2/3 A = {2, 4, 6} B = {1, 2} P(A B) = (3+2) – 1 = 4/6 = 2/3  

15. 12 27 18 33

16. a.Korea

17. a. Korea only

18. c. Japan or Hong Kong?

19. d. Korea and Hong Kong?

20. d. Hong Kong but not Japan?

21. Let’s Update the Scores

22. Assignment

23. Study the mutually and non mutually exclusive events