Set Notation And Probability Diagrams

9.A fair six-sided dice is rolled twice. What is the probability of getting a number greater than 4 both times?

10.In a class of 30 students, 15 study Spanish, 3 study both Spanish and German, and 7 study neither. How many study only German?

11.ℰ = {x: x is a positive integer less than 20}. A = {x: x is an even number}. B = {x: x is a multiple of 3}. What is n(A ∪ B)?

12.Ali rolls a fair six-sided dice twice. What is the probability that he gets a number greater than 4 at least once?

13.Bag A has 0.6 probability of green, bag B has 0.2 probability of green. One bead taken from each bag. What is the probability of getting one of each colour?

14.ℰ = {positive integers less than 16}. X = {prime numbers}. Y = {multiples of 3}. What is n(Y')?

15.ℰ = {natural numbers ≤ 15}. F = {factors of 12}. O = {odd numbers}. A number is chosen at random from ℰ. What is the probability it is in O?

16.A survey of 60 children is done. 24 like football, 19 like cricket, and 10 like football but not cricket. How many like both football and cricket?

17.The Venn diagram shows frequencies. Region A only: 10, A∩B: 5, B only: 8, neither: 2. What is P(A ∪ B)?

18.A bag contains 3 blue and 8 red counters. A counter is taken, replaced, then another taken. What is the probability of getting one of each colour?

19.In a two-way table, what does the number in the bottom-right corner represent?

20.ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. A = {1, 2, 3, 4}. B = {3, 4, 5, 6}. What is n(A ∩ B)?

21.Which of the following is the correct set notation for the complement of set A?

22.The two-way table shows the number of students studying Spanish or German in Year 12 and Year 13. What is the probability that a randomly selected student studies Spanish?

23.A bag contains 3 blue and 8 red counters. A counter is taken at random and replaced. Then another counter is taken. What is the probability that both counters are red?

24.ℰ = {1,2,3,4,5,6,7,8,9,10,11,12,13,14}. F = {x: x is a factor of 14}. P = {x: x is a prime number less than 14}. What is n(F ∪ P)?

25.Which symbol is used to represent the universal set?

26.What does n(A) represent?

27.In a Venn diagram, which region represents A ∩ B?

28.A tree diagram shows the probability of rain is 1/3. If it rains, the probability of going fishing is 3/5. If it does not rain, the probability of going fishing is 3/4. What is the probability that it rains and Amira goes fishing?

29.The complement of set A, written A', contains all elements in the universal set that are not in A.

30.In a two-way table, the number of students who study Spanish is 20 out of 55 total. What is the probability that a randomly selected student studies Spanish?

31.If P(A) = 0.6 and P(B) = 0.5, then P(A and B) must be 0.3.

32.Match each set notation to its correct description.

33.Arrange the following steps in the correct order to find the probability that a student chosen at random from a class studies Spanish, given that they are in Year 13, using a two-way table.

34.In a Venn diagram showing sets A and B, which of the following regions are shaded to represent A ∪ B? (Select all that apply)

35.In a probability tree diagram, the probabilities on branches that split from the same point must sum to 1.

36.The two-way table shows the number of students in Year 12 and Year 13 who study Spanish or German. A student is chosen at random from Year 12. What is the probability that they study German? | | Spanish | German | Total | |-------|---------|--------|-------| |Year 12| 15 | 10 | 25 | |Year 13| 5 | 25 | 30 | |Total | 20 | 35 | 55 |

37.The Venn diagram shows the number of elements in each region. What is P(A ∩ B)? A: 10 only, A∩B: 5, B: 8 only, Neither: 2

38.A coin is flipped and a fair six-sided dice is rolled. What is the probability of getting a head and a number greater than 4?

39.Write the set of positive integers less than 5 using curly bracket notation.

40.ℰ = {1,2,3,4,5,6,7,8,9,10}. A = {1,2,3,4}. B = {3,4,5,6}. What is n(A ∪ B)?

41.A fair six-sided dice is rolled twice. What is the probability of getting a 5 both times? Give your answer as a fraction in simplest form.

42.A bag contains 5 red and 3 blue counters. Two counters are taken at random without replacement. What is the probability that both counters are the same colour? Give your answer as a fraction in simplest form.

43.Complete the sentences using set notation.

44.ℰ = {1,2,3,4,5,6,7,8,9,10}. A = {1,2,3,4}. B = {3,4,5,6}. What is n(A ∪ B)?

45.A fair six-sided dice is rolled twice. What is the probability of getting a 5 both times? Give your answer as a fraction in simplest form.

46.A bag contains 5 red and 3 blue counters. Two counters are taken at random without replacement. What is the probability that both counters are the same colour? Give your answer as a fraction in simplest form.