07 Jan 2DA. Definition of probabilities

MATH221 Statistics for Decision Making

Week 2 Homework

Question 1 According to company records, the probability that a washing machine will break in the first year is 4%. This would be considered:

Homework Help:

2DA. Definition of probabilities and classical, empirical, subjective probabilities (Links to an external site.) (DOCX)

Classical probability

Subjective probability

Manufactured probability

Empirical probability

Question 2 Given the following information, find the probability that a randomly selected student will be very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21

Homework Help:

2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)

21.0%

28.8%

21.6%

39.4%

Question 3 Given the following information, find the probability that a randomly selected dog will be a golden retriever or a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles: 20, pugs: 38

Homework Help:

2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)

60.5%

46.9%

39.5%

58.0%

Question 4 Given that there is a 22% chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain) on the next two days?

Homework Help:

2VA: Probabilities given probability of success and 2 or more events (Links to an external site.) (0:51)

2DC. Probabilities given probability of success and 2 or more events (Links to an external site.) (DOCX)

13.4%

17.2%

1.1%

78.0%

Question 5 Consider the following table. What is the probability of red?

Red Blue Total

Yes 15 21 36

No 38 13 51

Total 53 34 87

Homework Help:

2VB: Conditional probabilities from a table (Links to an external site.) (1:45)

15/53

36/87

15/87

53/87

Question 6 Consider the following table. What is the probability of green, given no?

Red Blue Green Total

Yes 33 44 14 91

No 18 5 28 51

Total 51 49 42 142

Homework Help:

2VB: Conditional probabilities from a table (Links to an external site.) (1:45)

51/142

28/51

28/42

42/142

Question 7 A card is randomly selected from a standard deck of 52 cards. What is P(heart)?

Homework Help:

2VC: Probabilities when drawing one card from a deck (Links to an external site.) (0:59)

2DD. Probabilities when drawing one card from a deck (Links to an external site.) (DOCX)

26/52

13/52

1/52

4/52

Question 8 In a sample of 350 customers, 105 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?

Homework Help:

2VE: Probabilities of drawing several from many without replacement (Links to an external site.) (1:35)

2DE. Probabilities of drawing several from many without replacement (Links to an external site.) (DOCX)

9.00%

30.00%

8.94%

17.88%

Question 9 In a sample of 528 customers, 484 say they are happy with the service. If you select three customers without replacement for a commercial, what is the probability they will all say they are happy with the service?

Homework Help:

2VE: Probabilities of drawing several from many without replacement (Links to an external site.) (1:35)

2DE. Probabilities of drawing several from many without replacement (Links to an external site.) (DOCX)

91.67%

76.99%

77.03%

84.21%

Question 10 One event is a father being right handed. The other event is that his daughter is right handed. How would you classify these events?

Homework Help:

2DF. Independent versus dependent events; mutually exclusive and non-mutually exclusive events, complements (Links to an external site.) (DOCX)

Question 11 A company sells 14 types of crackers that they label varieties 1 through 14, based on spice level. What is the probability that one purchase results in a selection of a cracker with an even number or a number less than 5?

Homework Help:

2VF (1): Probabilities using addition rule from values and from percentages (Links to an external site.) (0:54)

2DG. Probabilities using addition rule (Links to an external site.) (DOCX)

71.4%

14.0%

64.3%

35.7%

Question 12 Of the shirts produced by a company, 6.5% have loose threads, 9.5% have crooked stitching, and 3% have loose threads and crooked stitching. Find the probability that a randomly selected shirt has loose threads or has crooked stitching.

Homework Help:

2VF (1): Probabilities using addition rule from values and from percentages (Links to an external site.) (0:54)

2DG. Probabilities using addition rule (Links to an external site.) (DOCX)

12.5%

19.0%

13.0%

16.0%

Question 13 Randomly select a customer that is a frequent shopper at our store. Randomly select a customer who does not know the store’s location. Are these events mutually exclusive?

Homework Help:

2DF. Independent versus dependent events; mutually exclusive and non-mutually exclusive events, complements (Links to an external site.) (DOCX)

Question 14 In a sample of 800 adults, 242 said that they liked sugar cereals. Three adults are selected at random without replacement. Find the probability that all three like sugar cereals.

Homework Help:

2VG: Probabilities of drawing several from many without replacement, all or none outcomes (Links to an external site.) (2:16)

2DH. Probabilities of drawing several from many without replacement, all or none outcomes (Links to an external site.) (DOCX)

2.70%

2.77%

2.73%

2.74%

Question 15 In a sample of 80 adults, 15 said that they would buy a car from a friend. Three adults are selected at random without replacement. Find the probability that none of the three would buy a car from a friend.

Homework Help:

2VG: Probabilities of drawing several from many without replacement, all or none outcomes (Links to an external site.) (2:16)

2DH. Probabilities of drawing several from many without replacement, all or none outcomes (Links to an external site.) (DOCX)

53.64%

53.16%

15.88%

17.27%

Question 16 A sock drawer has 17 folded pairs of socks, with 5 pairs of white, 8 pairs of black and 4 pairs of blue. What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair?

Homework Help:

2VH (1): Probability with multiplication rule from numbers and from probability outcomes (Links to an external site.) (1:30)

2VH (2): Probability with multiplication rule from numbers and from probability outcomes (Links to an external site.) (0:58)

2DI. Probability with multiplication rule (Links to an external site.) (DOCX)

52.94%

26.47%

24.91%

47.06%

Question 17 An investment advisor believes that there is a 28% chance of making money by investing in a specific stock. If the stock makes money, then there is a 43% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money and receive a dividend.

Homework Help:

2VH (1): Probability with multiplication rule from numbers and from probability outcomes (Links to an external site.) (1:30)

2VH (2): Probability with multiplication rule from numbers and from probability outcomes (Links to an external site.) (0:58)

2DI. Probability with multiplication rule (Links to an external site.) (DOCX)

43%

28%

12%

15%

Question 18 An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.

Homework Help:

2VH (1): Probability with multiplication rule from numbers and from probability outcomes (Links to an external site.) (1:30)

2VH (2): Probability with multiplication rule from numbers and from probability outcomes (Links to an external site.) (0:58)

2DI. Probability with multiplication rule (Links to an external site.) (DOCX)

16%

14%

30%

48%

Question 19 A smartphone company found in a survey that 20% of people did not own a smartphone, 28% owned a smartphone only, 14% owned a smartphone and only a tablet, 13% owned a smartphone and only a computer, and 25% owned all three. If a person were selected at random, what is the probability that the person would own a smartphone only or a smartphone and computer?

Homework Help:

2VF (2): Probabilities using addition rule from values and from percentages (Links to an external site.) (1:01)

2DG. Probabilities using addition rule (Links to an external site.) (DOCX)

80%

42%

41%

28%

Question 20 Match the terms and their definitions

Homework Help:

2DA. Definition of probabilities and classical, empirical, subjective probabilities (Links to an external site.) (DOCX)

2DF. Independent versus dependent events; mutually exclusive and non-mutually exclusive events, complements (Links to an external site.) (DOCX)

0 and 1

1 – P(E)

The occurrence of one event does not affect the occurrence of the other

Cannot occur at the same time

Probability of an event given that another event has occurred