A group of 1000 people are surveyed and asked two questions; whether they own a computer and whether they use a computer at their workplace. The results are presented here:

• 591 people own a computer and use a computer at work
• 150 people own a computer but do not use a computer at work
• 160 people do not own a computer but use a computer at work
• 99 people do not own a computer and do not use a computer at work

Define the events A and B to be:

• A: a randomly chosen person owns a computer
• B: a randomly chosen person doesnotuse a computer at work

Jessie was studying this situation and went about calculating the probability of the union of A and B. Jessie did this by counting up all of the different ways that A could occur, and then counting up all of the ways that B could occur. She then added these two numbers together and divided by 1000 to find P(A or B).

a)A contingency table for the survey is shown. The values have not been put into the table, but the cells have been marked C1, C2, C3, C4.

Use computer at work Own a computer

yes no

yes C1 C2

no C3 C4

In the method that Jessie uses to calculate P(A or B), the cell that is over-counted is cell:

A) C1

B) C2

C) C3

D) C4

b)Calculate the probability of the union A or B. Give your answer as a decimal to 2 decimal places.

P(A or B) =

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Craig owns a simple steakhouse restaurant, Pull Up Steaks, and he is thinking of making some changes: he wants to broaden the menu and he wants to put a bar in the restaurant. One weekend he hands out the following questionnaire to the diners:

FEEDBACK

How were we?

Here at Pull Up Steaks our number one priority is your dining satisfaction and we are always trying to find new ways of achieving this. So we have a couple of questions ...

Do you think we should expand our menu? YES / NO

Do you think we should include a bar in our restaurant? YES / NO

Craig gets 248 responses. The results of this survey are displayed in the following contingency table:

Restaurant Bar

Menu Expansion Yes No

Yes 44 20

No 127 57

Complete these statements using the information in the above table. Give your answers to parts a) and b) to the nearest whole number. Give your answer to part c) as a decimal to 2 decimal places.

a)The number of respondents thatdo notwant the restaurant bar is__________.

b)The number of respondents that want at least one of the changes that Craig has proposed is_________.

c)The probability that a respondent chosen at random will want at least one of the changes that Craig has proposed is___________.

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A student at a university has been doing a project to investigate entertainment habits of students. They have surveyed 100 random students who were each asked three questions:

1. Have you watched a movie in the last week?
2. Have you listened to music in the last week?
3. Have you read a book in the last week?

However, the student keeps a very messy room and has lost some of the results. They have been able to find the following results:

Of all the students surveyed, 43 had watched a movie, 37 had listened to music and 46 had read a book in the last week. Also:

• 5 students answered yes to all three questions
• 10 students answered yes to questions 1 and 2 only
• 12 students answered yes to questions 1 and 3 only
• 16 students answered yes only to question 1
• 17 students answered no to all three questions

Find the missing information and answer the following questions regarding the group surveyed. Give your answers as whole numbers.

Calculate the number of students that: __________

a)answered yes to question 2 or 3 but no to question 1 =_________

b)answered yes to exactly two questions =_________

c)had watched a movie or read a book but had not listened to music =__________