In a region, 12% of the adult population are smokers, 0.8% are smokers with emphysema, and...

In a region, 12% of the adult population are smokers, 0.8% are smokers with emphysema, and 0.2% are non-smokers with emphysema.

a. What is the probability that a person selected at random has emphysema?

b. Given that the selected person is a smoker, what is the probability that the person has emphysema?

c. Given that the selected person is not a smoker, what is the probability that this person has emphysema?

Solutions

Expert Solution

P(smokers) = 0.12 and therefore, P(non - smokers) = 1 - P(smokers) = 1 - 0.12 = 0.88

P(smokers and emphysema) = 0.008

P(non - smokers and emphysema) = 0.002

a. Answer :

P(emphysema) = P(smokers and emphysema) + P(non - smokers and emphysema)

= 0.008 + 0.002

= 0.01

Therefore, the probability that a person selected at random has emphysema is 0.01

b. Answer :

P(emphysema | smoker) = P(emphysema and smoker) / P(smoker) ...........(conditional probability)

= 0.008 / 0.12

= 0.0667

Therefore, given that the selected person is a smoker, the probability that the person has emphysema is 0.0667

c. Answer :

P(emphysema | non - smoker) = P(emphysema and non - smoker) / P(non - smoker) ..........(conditional probability)

= 0.002 / 0.88

= 0.0023

Therefore, given that the selected person is not a smoker, the probability that this person has emphysema is 0.0023

orchestra answered 1 year ago

Next > < Previous

Related Solutions

1) 75% of adult smokers started smoking before turning 18 years in a population. A random...

1) 75% of adult smokers started smoking before turning 18 years in a population. A random sample of 30 smokers 18 years or older are selected and the number of smokers who started smoking before 18 is recorded. 1) Find the probability that exactly 7 are smokers. 2) Find the probability that at least 5 are smokers. 3) Find the probability that fewer than 3 are smokers. 4) Find the probability that between 4 and 7 of them, inclusive, are smokers. 5) Find the mean...

In a specific population of people, cancer is found in 0.8% of the people. If a...

In a specific population of people, cancer is found in 0.8% of the people. If a person does have the disease, a diagnostic procedure will identify the presence of cancer in 93% of such people. If a person does not have cancer, this diagnostic procedure will give a false-positive result 0.3% of time. What is the probability that a person with a positive test result has cancer.

A research team conducted a survey in which the subjects were adult smokers. Each subject in...

A research team conducted a survey in which the subjects were adult smokers. Each subject in a sample of 200 was asked to indicate the extent to which he or she agreed with the statement. “I would like to quit smoking”. The results were as follows. Strongly Agree: 102 Agree: 30 Disagree: 60 Strongly disagree: 8 Can one conclude on the basis of these data that, in the sampled population, opinions are not equally distributed over the four levels of...

10 KEY Region 1 = NW Population 1 = Under 50,000 Region 2 = SW Population...

10 KEY Region 1 = NW Population 1 = Under 50,000 Region 2 = SW Population 2 = 50,000 - 100,000 Region 3 = NE Population 3 = Over 100,000 Region 4 = SE Count of Population Region Total Population 1 2 3 4 1 28 56 33 36 153 2 36 36 44 31 147 3 36 48 34 32 150 Total: 100 140 111 99 450 Big Burger is a fast food restaurant that has 450...

According to a study, 50 % of adult smokers started smoking before 21 years old. 14...

According to a study, 50 % of adult smokers started smoking before 21 years old. 14 smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. 1. The probability that at least 4 of them started smoking before 21 years of age is? 2. The probability that at most 8 of them started smoking before 21 years of age is? 3. The probability that exactly 2 of them started...

According to an almanac, 70% of adult smokers started smoking before turning 18 years old. (a)...

According to an almanac, 70% of adult smokers started smoking before turning 18 years old. (a) If 300 adult smokers are randomly selected, how many would we expect to have started smoking before turning 18 years old? (b) Would it be unusual to observe 255 smokers who started smoking before turning 18 years old in a random sample of 300 adult smokers? Why?

According to a recent study, 10 % of adult smokers started smoking before 21 years old....

According to a recent study, 10 % of adult smokers started smoking before 21 years old. A random sample of 6 smokers age 21 years or older is selected, and the number of smokers who started smoking before 21 is recorded. Calculate the following probabilities. Round solutions to four decimal places, if necessary. 1. The probability that at least 3 of them started smoking before 21 years of age is P(x≥3)= 2. The probability that at most 4 of them...

QUESTION 10 What is the 95% confidence interval for the proportion of smokers in the population...

QUESTION 10 What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)? QUESTION 8 Question 8-10 are based on the following information: The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .35. How large a sample...

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less...

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of...

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less...

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 7%probability that a nonsmoker will begin smoking a pack or less per day, and a 3% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting...

Subjects