Three-Set Venn Diagram Construction

1. A group of 200 adults were asked whether they read cooking magazines, travel magazines or sport magazines.
   Their replies showed that

• 29 read only cooking magazines
• 33 read only travel magazines
• 42 read only sport magazines
• 17 read cooking magazines and sport magazines but not travel magazines
• 11 read travel magazines and sport magazines but not cooking magazines
• 22 read cooking magazines and travel magazines but not sport magazines
• 32 do not read cooking magazines, travel magazines or sport magazines
  1. Using this information, complete the Venn diagram on page 11

One of these adults was chosen at random.

Find the probability that this adult,

1. reads cooking magazines and travel magazines and sport magazines,
2. does not read cooking magazines. Given that this adult reads travel magazines,

find the probability that this adult also reads sport magazines.

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There are 180 students at a college following a general course in computing. Students on this course can choose to take up to three extra options. 112 take systems support, 70 take developing software, 81 take networking, 35 take developing software and systems support, 28 take networking and developing software, 40 take systems support and networking, 4 take all three extra options.

1. In the space below, draw a Venn diagram to represent this information. [5]

A student from the course is chosen at random. Find the probability that this student takes

1. none of the three extra options, [1]
2. networking only. [1]

Students who want to become technicians take systems support and networking. Given that a randomly chosen student wants to become a technician,

1. find the probability that this student takes all three extra options. [2]

A sample of 240 households were asked which, if any, of the following animals they own as pets: • cats (C) • dogs (D) • tortoises (T) The results are shown in the table below.

1. Represent this information by fully completing the Venn diagram below. [3 marks] \includegraphics{figure_16}
2. A household is chosen at random from the sample.
   1. Find the probability that the household owns a cat only. [1 mark]
   2. Find the probability that the household owns at least two of the three types of pet. [2 marks]
   3. Find the probability that the household owns a cat or a dog or both, given that the household does not own a tortoise. [2 marks]
3. Determine whether a household owning a cat and a household owning a tortoise are independent of each other. Fully justify your answer. [2 marks]