The document discusses various probability scenarios involving shuffled number cards and events related to multiples and categories of numbers. It includes calculations for probabilities such as the likelihood of selecting a multiple of 3 or 4, even or odd numbers, and the outcomes of drawing marbles or letters from specific sets. Additionally, it covers group activities for solving related probability problems.

2. •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:

3. 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

4. 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

5. 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

6. 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

7. 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 𝑈 B) = (6 + 12) - 2 = 16/30 = 8/15

8. 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

10. 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.

12. 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.

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

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

15. 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

16. 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

17. 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(A𝑈B) = (3+2) – 1 = 4/6 = 2/3

22. 12
27
18 33

27. a.Korea

28. a. Korea only

29. c. Japan or Hong Kong?

30. d. Korea and Hong Kong?

31. d. Hong Kong but not
Japan?

32. Let’s Update the Scores

35. Assignment

36. Study the mutually and non
mutually exclusive events