# Question 9

9.1 For any two events, A and B, it is given that P(A) = 0,48 and P(B) = 0,26.

Determine:

9.1.1 P(A and B) if A and B are independent events (2)

9.1.2 P(A or B) if A and B are mutually exclusive events (2)

9.2 A survey was conducted among 130 Grade 11 learners to establish which snack they prefer to eat while they watch television. The results were summarized in the Venn diagram below. However, some information is missing.

9.2.1 If 29 learners prefer at least two types of snacks, calculate the value of x and y. (4)

9.2.2 Determine the probability that a learner who does not eat nuts will either have another snack or no snack while watching television. (3)

9.3 A group of 200 tourists visited the same restaurant on two consecutive evenings. On both evenings, the tourists could either choose beef (B) or chicken (C) for their main meal. The manager observed that 35% of the tourists chose beef on the first evening and 70% of them chose chicken on the second evening.

9.3.1 Draw a tree diagram to represent the different choices of main meals made on the two evenings. Show on your diagram the probabilities associated with each branch as well as all the possible outcomes of the choices. (4)

9.3.2 Calculate the number of tourists who chose the same main meal on both evenings.

9.3.3 Show that more tourists opted not to change their choice of main meal during their two visits to the restaurant. (2) [20]

TOTAL: 150