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Think and Answer requires you to answer two questions

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Think and Answer requires you to answer two questions. For each question, do not simply provide an answer; make sure you explain how you arrived at that answer. Even if your reasoning is wrong, you will still be credited for participation.

Answer the following question:

1. The weather forecast for the next day was 90% chance of rain. On the next day, the skies were clear. Can we say the forecast was wrong? Why or why not?

True or False?

2. It is known that 10% of people are left-handed. This means that in a randomly selected group of 20 persons two must be left-handed.

3. If you have 5 suits, 8 shirts and 9 neckties, you can come to work each time in a different outfit during the whole year.

4. A coin is flipped twice. P(two heads) + P(two tails) = 1.

HW 2 Ch. 4

Sec 4.1:

2. ProbabilityRewrite the following statement so that the likelihood of rain is expressed as a value between 0 and 1: “The probability of rain today is 25%.”

5. Identifying Probability Values Which of the following are probabilities?

 0  3/5  5/3 -.025 25% 7:3 1 50-50 5:1 0.135 2.017

In Exercises 9–12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.

9. 47 girls.
    
10. 26 girls.
     
11. 23 girls.
     
12. 5 girls.

In Exercises 13–20, express the indicated degree of likelihood as a probability value ­between 0 and 1.

13. Testing If you make a random guess for the answer to a true/false test question, there is a 50–50 chance of being correct.
     
14. SAT Test When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.
     
15. Luggage Based on a Harris poll, if you randomly select a traveler, there is a 43% chance that his or her luggage is black. 

In Exercises 25–32, find the probability and answer the questions.

27. Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected value of 3/4, as Mendel claimed?
 

28. Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.

• • What is the probability that Mike will guess correctly? (Ignore leap years.)
  • Would it be unlikely for him to guess correctly on his first try?
  • If you were Kelly, and Mike did guess correctly on his first try, would you believe his claim that he made a lucky guess, or would you be convinced that he already knew when you were born?

If Kelly asks Mike to guess her age, and Mike’s guess is too high by 15 years, what is the probability that Mike and Kelly will have a second date?

 

Probability from a Sample Space. In Exercises 33–36, use the given sample space or construct the required sample space to find the indicated probability.

 

34. Three Children Using the same sample space and assumption from Exercise 33, find the probability that when a couple has three children, there are exactly two girls.

Using Probability to Form Conclusions. In Exercises 37–40, use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.

37.Predicting Gender A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant women, 57 correctly predicted the gender of their baby (based on data from “Are Women Carrying ‘Basketballs’. . ., ” by Perry, DiPietro, Constigan, Birth, Vol. 26, No. 3). If pregnant women have no such ability, there is a 0.327 probability of getting such sample results by chance. What do you ­conclude?

 

39. Coffee Talk A study on the enhancing effect of coffee on long-term memory found that 35 participants given 200 mg of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine.

• There was a probability of 0.049 that the difference between the coffee group and the placebo group was due to chance. What do you conclude?

A group given a higher dose of 300 mg performed better than the 200 mg group, with a probability of 0.75 that this difference is due to chance. What do you conclude?

 

 

4.2:

1. Notation When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and P(-overA) represent?
2. Notation When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M\B) represent? Is P(M\B) the same as P(M\B)?
3. Sample for a Poll There are 15,524,971 adults in Florida. If the Gallup organization randomly selects 1068 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as being independent for the purposes of calculations?
4. Rule of Complements When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write sentence describing what the rule of complements is telling us: P (B or -over B)= 1.

Finding Complements. In Exercises 5–8, find the indicated complements.

 6. Flights According to the Bureau of Transportation, 80.3% of American Airlines flights arrive on time. What is the probability of randomly selecting an American Airlines flight that does not arrive on time?

 

In Exercises 9–20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

	McDonald’s	Burger King	Wendy’s	Taco Bell
Order Accurate	329	264	249	145
Order Not Accurate	33	54	31	13

9. Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting food that is not from McDonald’s.
10. Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order that is not accurate.
11. Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order from McDonald’s or an order that is accurate. Are the events of selecting an order from McDonald’s and selecting an accurate order disjoint events?

 13. Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that they are both from Taco Bell.

Assume that the selections are made with replacement. Are the events independent?

Assume that the selections are made without replacement. Are the events independent?

 

14. Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that both of them are not accurate.

Assume that the selections are made with replacement. Are the events independent?

Assume that the selections are made without replacement. Are the events independent? 

17. Fast Food Drive-Thru Accuracy If one order is selected, find the probability of getting an order from McDonald’s or Wendy’s or an order that is not accurate.

 

Redundancy. Exercises 25 and 26 involve redundancy.

25. Redundancy in Computer Hard Drives It is generally recognized that it is wise to back up computer data. Assume that there is a 3% rate of disk drive failure in a year (based on data from various sources, including lifehacker.com).
    • If you store all of your computer data on a single hard disk drive, what is the probability that the drive will fail during a year?
    • If all of your computer data are stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that both drives will fail during a year?
    • If copies of all of your computer data are stored on three independent hard disk drives, what is the probability that all three will fail during a year?

Describe the improved reliability that is gained with backup drives.

 

Sec 4.3:

 

1. Language: Complement of “At Least One” Let A = the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing event -over A
    
2. Probability of At Least One Let A = the event of getting at least 1 defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If 5% of the iPhones in a batch are defective and the other 95% are all good, which of the following are correct?

                     a. P(-over A)=(0.95)(0.95)=0.857

                     b.P(A) = 1 ? (0.95)(0.95)(0.95) = 0.143

                     c.P(A) = (0.05)(0.05)(0.05) = 0.000125

 

At Least One. In Exercises 5–12, find the probability.

5. Three Girls Find the probability that when a couple has three children, at least one of them is a girl. (Assume that boys and girls are equally likely.)
    
6. Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.
    

7. Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). Among the next six randomly selected births in the United States, what is the probability that at least one of them is a girl?

10. At Least One Correct Answer If you make random guesses for 10 multiple choice SAT test questions (each with five possible answers), what is the probability of getting at least 1 correct? If these questions are part of a practice test and an instructor says that you must get at least one correct answer before continuing, is there a good chance you will continue?

Denomination Effect. In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters or a $1 bill, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

	Purchased Gum	Kept the Money
Students Given Four Quarters	27	16
Students Given a $1 bill	12	34

 

13. Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

c. What do the preceding results suggest?

 

14. Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.

c. What do the preceding results suggest?

15. Denomination Effect

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.

c. What do the preceding results suggest?

 

Sec 4.4

 

In Exercises 5–36, express all probabilities as fractions.

5. ATM Pin Numbers A thief steals an ATM card and must randomly guess the correct pin code that consists of four digits (each 0 through 9) that must be entered in the correct order. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

 

8. Soccer Shootout In soccer, a tie at the end of regulation time leads to a shootout by three members from each team. How many ways can 3 players be selected from 11 players available? For 3 selected players, how many ways can they be designated as first, second, and third?
 

9. Grading Exams Your professor has just collected eight different statistics exams. If these exams are graded in random order, what is the probability that they are graded in alphabetical order of the students who took the exam?

 

21. Phone Numbers Current rules for telephone area codes allow the use of digits 2–9 for the first digit, and 0–9 for the second and third digits. How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately preceding the last four digits of a phone number. Given both of those rules, how many 10-digit phone numbers are possible? Given that these rules apply to the United States and Canada and a few islands, are there enough possible phone numbers? (Assume that the combined population is about 400,000,000.)

 

28. Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.

1. 1. If the subjects are selected and treated one at a time in sequence, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available?
   2. If 14 subjects are selected from the 16 that are available, and the 14 selected subjects are all treated at the same time, how many different treatment groups are possible?
   3. If 14 subjects are randomly selected and treated at the same time, what is the probability of selecting the 14 youngest subjects?

 

 

 34.  Counting with Fingers How many different ways can you touch two or more fingers to each other on one hand?