HW 5

About​ 12% of men and​ 10% of women are​ left-handed. If a person is selected at​ random, are the event that the person is male and the event that the person is​ left-handed independent or​ associated?

A. Gender and handedness are associated because men are more likely to be​ left-handed than women

Assume a person is selected randomly from the group of people represented in the table shown below. The probability that the person says No given that the person is a man is 57/554​, or 10.3​%. The probability that the person is a man given that the person says No is 57/101 or 56.4​%, and the probability that the person says No and is a man is 57/1282 or 4.4​%. Why is the last probability the​ smallest?

B. The last probability is the smallest because it is finding the proportion of people who said No and are a man from all of the​ respondents, not just a subset of them.

A person was trying to figure out the probability of getting two heads when flipping two coins. He flipped two coins 10 times, and in 4 of these 10 times, both coins landed heads. On the basis of this​ outcome, he claims that the probability of two heads is 4​/10​, or 40​%. Is this an example of an empirical probability or a theoretical​ probability? Explain.

B. This is an example of empirical probability because it is based on an experiment.

A bag of candy contains 10 red candies and 10 brown candies. A friend says the probability of reaching in the bag without looking and pulling out a red candy is 50​% because 10 out of 20 candies are red. Is this an example of an empirical probability or a theoretical​ probability?

B. This is an example of theoretical probability because it is not based on an experiment.

A poll asked respondents if they had taken a vacation in the last year. The respondents were separated into two​ groups: those who had graduated from college and those who had not. Numbers are based on a sample size of 250 in each group. Suppose one person is selected at random form this group. Name a pair of events that are not mutually exclusive.

C. Being a college graduate and saying Yes are not mutually exclusive.

A report asked people who got their news from television which television sector they relied on primarily for their​ news: local​ TV, network​ TV, or cable TV. The results were used to generate the data in the table below. Determine whether being female is independent of choice of local TV. Explain your answer in the context of this problem.

Since P(female / local) = 56.2% and P(female) = 54.7%, the events are not independent.

A college conducted a student survey to learn about commute patterns. Students were given a choice of three​ options: car,​ bus, or other. When looking at the survey​ results, 36​% of students responded​ "car," and 29​% responded​ "bus." Assuming all students answered this survey​ question, what percentage of the students responded​ "other"?

The percentage of the students that responded​ "other" was 35%.

According to a recent​ study, 58​% of households from a certain large region no longer have a landline and instead only have cell phone service. Suppose three households from the region are selected at random. a. What is the probability that all three have only cell phone​ service? b. What is the probability that at least one has only cell phone​ service?

a. The probability that all three have only cell phone service is .1951 b. The probability that at least one has only cell phone service is .9251

If we flip a coin 10​ times, what percentage of the time will the coin land on​ heads? A first step to answering this question is to simulate 10 flips. Use the accompanying random number table to simulate flipping a coin 10 times. Let the digits​ 0, 1,​ 2, 3, 4 represent heads and the digits​ 5, 6,​ 7, 8, 9 represent tails. Begin with the first digit in the third row of the random number table. a. Write the sequence of 10 random digits. b. Change the sequence of 10 random digits to a sequence of heads and​ tails, writing H for the digits​ 0, 1,​ 2, 3, 4 and the T for the digits​ 5, 6,​ 7, 8, 9. What was the longest streak of heads in your​ list? c. What percentage of the flips were​ heads?

a. The sequence of digits is 3​, 5​, 9​, 6​, 3​, 7​, 1​, 0​, 2​, 7. b. The sequence of letters is H, T, T, T, H, T, H, H, H, T. The longest streak of heads was 3 head(s). c. The percentage of flips that were heads is 50%

A poll asked respondents to fill in the blank to this​ question: Compared to other industries there is​ ____ discrimination against women in the tech industry. Responses separated by gender are shown in the following table. The results are shown using a sample size of 274 men and 139 women. Complete parts​ (a) and​ (b) below. a. What is the probability that a randomly selected person is a woman and said​ "more"? b. What is the probability that a randomly selected person is a woman or said​ "more" (or​ both)?

a.) 10.9% b.) 47.5%

A recent poll asked respondents to fill in the blank to this​ question: "The country​ ____ when it comes to giving equal rights to​ women" with one of three choices. The results are shown in the accompanying table using a sample size of 120 men and 120 women. Complete parts a and b below. a. A person is selected randomly from the entire group. We want to find the probability that the person selected is a female who said "has been about right​." Which of the following statements best describes the​ question? b. Find the probability that a person randomly selected from the entire group is a female who responded "has been about right​."

a.) A. P(female and responded "has been about right") b.) The probability is 11/60.

A study found that highly experienced teachers may be associated with higher student achievement. Suppose​ fourth-grade students at an elementary school are randomly assigned to one of eight teachers. Teachers Garcia, Lopez, Hernandez, and Smith are considered highly experienced. Teachers Perry, Crouse, Lee, and Lee are considered less experienced. Complete parts​ (a) through​ (c) below. a. List the equally likely outcomes that could occur when a student is assigned to a teacher. Choose the correct answer below. b. What is the probability that a​ fourth-grade student at this school is assigned to a highly experienced​ teacher? c. What event is the complement of the event described in part​ (b)? What is the probability of this​ event? Select the correct choice below and fill in the answer box to complete your choice.

a.) D. Perry​, Garcia​, Crouse​, Lopez​, Lee​, Hernandez​, Smith​, and Lee b.) 50% c.) B. The complement is the probability that a​ fourth-grade student at this school is assigned to a less experienced teacher. The probability of this event is 50​%.

In a standard deck of playing cards there are four​ suits: clubs,​ diamonds, hearts, and​ spades, and the following cards appear in each​ suit: Ace,​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, Jack,​ Queen, King. The​ Jack, Queen, and King are called face cards because they have a drawing of a face on them. Diamonds and hearts are​ red, and clubs and spades are black. If you draw 1 card randomly from a standard​ 52-card playing​ deck, what is the probability of​ drawing: a. A 4​? b. A black ​card? c. A spade​? d. A non-face ​card? e. A jack or queen​?

a.) The probability of drawing a 4 is one 1/13 b.) The probability of drawing a black card is 1/2 c.) The probability of drawing a spade is 1/4 d.) The probability of drawing a non-face card is 10/13 e.) The probability of drawing a jack or queen is 2/13

An exam consists of 13 ​multiple-choice questions. Each of the 13 answers is either right or wrong. Suppose the probability that a student makes fewer than 4 mistakes on the exam is 0.45 and that the probability that a student makes from 4 to 8 ​(inclusive) mistakes is 0.29. Find the probability of each of the following outcomes. a. A student makes more than 8 mistakes b. A student makes 4 or more mistakes c. A student makes at most 8 mistakes d. Which two of these three events are​ complementary?

a.) The probability that a student makes more than 8 mistakes is .26. b.) The probability that a student makes 4 or more mistakes is .55. c.) The probability that a student makes at most 8 mistakes is .74. d.) B. At most 8 mistakes C. More than 8 mistakes

A poll asked a sample of adults if they had read a book in any format in the previous 12 months. The results are shown in the table below. Complete parts​ (a) and​ (b) below. a. If a person is randomly selected from this​ group, find the probability for parts​ (i) though​ (iii). i. the person is male ii. the person has read a book in the previous 12 months iii. the person is a male and has read a book in the previous 12 months b. Which group is more likely to have read a book in the previous 12​ months: men or​ women? Support your answer with appropriate statistics. Select the correct choice below and fill in the answer box within your choice.

a.) i. 52.7% ii. 72.3% iii. 36.1% b.) A. The women are more likely to have read a book in the previous 12 months because 76.6​% of the women read a book in the previous 12​ months, whereas 68.4​% of the men read a book in the previous 12 months.