4.3

1) 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

ANSWER:_____

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

P(A or B) =______

2) 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:

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:

Menu Expansion --- Restaurant Bar

--- Yes N0

Yes 44 127

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_____.

3) 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 =______

5.2

1) Fran is about to sit a multiple choice test with 10 questions. She has studied quite hard, and believes that the probability that she will get any particular question correct is 0.85. Fran also believes that the questions are independent, and her performance on each question is independent of her performance on any other question. Fran's parents tell her that if she gets at least 9 of the 10 questions correct, they will buy her a gift.

Based on this information, calculate the probability that Fran will get the gift. Give your answer as a decimal to 2 decimal places.

Probability =_____

2) You are a day trader on the stock exchange and you have invested all of your life savings in a portfolio containing 6 stocks. After dwelling on the risks involved in your investment, you have come to the conclusion that if at least half of the stocks in your portfolio are profitable, your investment will be a success.

Based on empirical data available from the historical records of the stock exchange, you believe that the probability of a stock being profitable is 0.45. Assuming that the profitability of each stock is independent of all the other stocks, calculate the probability (P(S)) that your investment is a success. Give your answer as a decimal to 2 decimal places.

P(S) =________

3) Ken is a factory worker, who is a part-time statistics student, and makes toys. He knows that the probability that any given toy on the factory line is faulty is a constant and is independent of whether or not any other toy on the line is faulty. This probability is 0.0870 (when rounded to 4 decimal places). Each day, Ken tests the same number of toys. He knows that the expected number of faulty toys each day is 34.

Given this information, calculate the number of toys that Ken tests each day. Give your answer as a whole number.

Number of toys Ken tests each day =_______