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Problem 5.1.20a
Using Probabilities for Significant Events
a. Find the probability of getting exactly 1 match.
Problem 5.2.13a
Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.
Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.
a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third is correct. That is, find P(WWC), where W denotes a wrong answer and C denotes a correct answer.
Problem 5.2.32a
In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments).
Hybrids Assume that offspring peas are randomly selected in groups of 16.
a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 16.
Problem 5b
In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.
Hurricanes
b. In a 118-year period, how many years are expected to have 7 hurricanes?
Problem 5.2.40b
One of Mendel’s famous experiments with peas resulted in 580 offspring, and 152 of them were yellow peas. Mendel claimed that under the same conditions, 25% of offspring peas would be yellow. Assume that Mendel’s claim of 25% is true, and assume that a sample consists of 580 offspring peas.
b. Find the probability of exactly 152 yellow peas.
Problem 5.2.29b
In Exercises 29 and 30, assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.
Gender Selection Assume that the groups consist of 36 couples.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Problem 5.3.7b
In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.
b. In a 118-year period, how many years are expected to have no hurricanes?
Problem 5.1.29b
Expected Value for the Florida Pick 3 Lottery In the Florida Pick 3 lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500.
b. What is the probability of winning?
Problem 5.3.8b
In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.
b. In a 118-year period, how many years are expected to have 10 hurricanes?
Problem 5.2.13b
Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.
Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.
b. Beginning with WWC, make a complete list of the different possible arrangements of two wrong answers and one correct answer, and then find the probability for each entry in the list.
Problem 5.2.32b
In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments).
Hybrids Assume that offspring peas are randomly selected in groups of 16.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Problem 5.3.9b
In Exercises 9–16, use the Poisson distribution to find the indicated probabilities.
Births In a recent year (365 days), NYU-Langone Medical Center had 5942 births.
b. Find the probability that in a single day, there are 16 births.
Problem 5.1.18b
Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).
Using Probabilities for Significant Events
b. Find the probability of getting 2 or more matches.
Problem 5.1.19b
Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet).
Using Probabilities for Significant Events
b. Find the probability of getting 3 or more matches.
Problem 5.2.28b
In Exercises 25–28, find the probabilities and answer the questions.
Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
Problem 5.2.38b
Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.
b. Find the probability of exactly 40 first lines for Democrats.
Problem 5.1.20b
Using Probabilities for Significant Events
b. Find the probability of getting 1 or fewer matches.
Problem 5.c.4a
Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.
a. 29% of the respondents reported that they negotiated salary at their latest job. What is the number of respondents who reported that they negotiated salary?
Problem 5.2.32c
In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments).
Hybrids Assume that offspring peas are randomly selected in groups of 16.
c. Is a result of 7 peas with green pods a result that is significantly low? Why or why not?
Problem 5.1.19c
Using Probabilities for Significant Events
c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?
Problem 5.c.8
Happiness In a survey sponsored by Coca-Cola, subjects were asked what contributes most to their happiness, and the table summarizes their responses. Does the table represent a probability distribution? Explain.
Problem 5.2.13c
Binomial Probability Formula. In Exercises 13 and 14, answer the questions designed to help understand the rationale for the binomial probability formula.
Guessing Answers Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions.
c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made?
Problem 5.1.20c
Using Probabilities for Significant Events
c. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)?
Problem 5.c.3d
Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.
d. If 1 of the 945 challenges is randomly selected, find the probability that it was made by a man or was upheld with an overturned call.
Problem 5.c.1e
Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.
0 0 1 2 17 28 21 8
e. Find the standard deviation.
f. Find the variance.
Problem 5.2.27c
In Exercises 25–28, find the probabilities and answer the questions.
Internet Voting Based on a Consumer Reports survey, 39% of likely voters would be willing to vote by Internet instead of the in-person traditional method of voting. For each of the following, assume that 15 likely voters are randomly selected.
c. Find the probability that at least one of the selected likely voters would do Internet voting.
Problem 5.c.4b
Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.
b. Among those who negotiated salary, 84% received higher pay. How many received higher pay?
Problem 5.2.38c
Politics The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning the order in which candidates’ names appeared on voting ballots. Among 41 different ballots, Democrats were assigned the desirable first line 40 times. Assume that Democrats and Republicans are assigned the first line using a method of random selection so that they are equally likely to get that first line.
c. Find the probability of 40 or more first lines for Democrats.
Problem 5.2.28c
In Exercises 25–28, find the probabilities and answer the questions.
Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Problem 5.c.3e
Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.
e. If one of the challenges is randomly selected, find the probability that it was made by a man, given that the challenge was upheld with an overturned call.
