Exam 9: Independence and Conditional Probabilities

During winter, red foxes hunt small rodents by jumping into thick snow cover, without any visual clue. Researchers examined the compass direction of hundreds of such jumps. They found that 73% of jumps in the northeast direction were successful, compared with 60% of jumps in the southwest direction and only 18% of jumps in all other directions. The value 73%, or 0.73, corresponds to which of the following probabilities?

For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the probability of selecting a wolf that is female, given that it hunts in a medium-sized pack?

Obesity is a growing public health concern worldwide. Adults with a body mass index (BMI) of 25 or greater are considered overweight or obese. The following table shows the number of adults (in millions) who are overweight or obese in countries with different income levels, based on data from the World Health Organization and the United Nations: ? ? Country income level Adults with high BMI (in millions) Adults with BMI < (in millions) Total High 549 414 963 Upper middle 612 1042 1654 Lower middle 288 1083 1371 Low 63 357 420 All 1512 2896 4408 What is the probability that an adult has a high BMI, given that the adult lives in a high-income country?

For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs or that are not female but hunt in medium-sized packs?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 50s who takes a mammography to screen for breast cancer: What percent of women in their 50s taking a screening mammography receive a positive test result?

Obesity is a growing public health concern worldwide. Adults with a body mass index (BMI) of 25 or greater are considered overweight or obese. The following table shows the number of adults (in millions) who are overweight or obese in countries with different income levels, based on data from the World Health Organization and the United Nations: ? ? Country income level Adults with high BMI (in millions) Adults with BMI < (in millions) Total High 549 414 963 Upper middle 612 1042 1654 Lower middle 288 1083 1371 Low 63 357 420 All 1512 2896 4408 What is the probability, P(high BMI | low-income country)?

Gallup reports that 30% of American adults have high blood pressure. A medical office selects at random two unrelated medical records from the practice's adult patients. What is the probability that at least 1 patient has high blood pressure?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 40s who takes a mammography to screen for breast cancer: If a randomly chosen woman in her 40s taking the mammography screening test gets a positive test result, the probability that she indeed has breast cancer is the positive predicted value, PPV = P(Cancer | Positive test). What is the PPV for this age group?

A researcher cross-classified 386 trout into groups based on their species (all were in genus Salmo) and gender: ? ? Species Female Male Brown 68 56 Flathead 91 40 Ohrid 5 6 Sevan 61 59 A trout is to be selected at random. What is the probability that the selected trout is a flathead trout?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 40s who takes a mammography to screen for breast cancer: The sensitivity of a diagnosis test is its ability to appropriately give a positive result when a person tested has the disease, P(Positive test | Cancer). What is the sensitivity of mammography?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 40s who takes a mammography to screen for breast cancer: A false negative happens when someone getting a mammography does have cancer and receives a negative test. What percent of women in their 40s taking a screening mammography receive a false negative?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 50s who takes a mammography to screen for breast cancer: If a randomly chosen woman in her 50s taking the mammography screening test gets a positive test result, the probability that she indeed has breast cancer is the positive predicted value, PPV = P(Cancer | Positive test). What is the PPV for this age group?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 40s who takes a mammography to screen for breast cancer: The specificity of a diagnosis test is its ability to appropriately give a negative result when a person tested doesn't have the disease, P(Negative test | No cancer). What is the specificity of mammography?

Obesity is a growing public health concern worldwide. Adults with a body mass index (BMI) of 25 or greater are considered overweight or obese. The following table shows the number of adults (in millions) who are overweight or obese in countries with different income levels, based on data from the World Health Organization and the United Nations: ? ? Country income level Adults with high BMI (in millions) Adults with BMI < (in millions) Total High 549 414 963 Upper middle 612 1042 1654 Lower middle 288 1083 1371 Low 63 357 420 All 1512 2896 4408 Which of the following options correctly describes country income level and BMI type?

Disjoint events are independent.

A recent nationwide study of myopia (nearsightedness) found that 38.1% of U.S. adults ages 18 to 24 suffer from myopia. Consider two young adults between the ages of 18 and 24, chosen randomly and independently. What is the probability that both individuals have myopia?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 50s who takes a mammography to screen for breast cancer: A false positive happens when someone getting a mammography does not have cancer and receives a positive test. What percent of women in their 50s taking a screening mammography receive a false positive?

The incidence of breast cancer varies depending on a woman's age. The National Cancer Institute gives the following probabilities for a randomly chosen woman in her 40s who takes a mammography to screen for breast cancer: A true positive happens when someone getting a mammography has cancer and receives a positive test result. What percent of women in their 40s taking a screening mammography receive a true positive?

A researcher cross-classified 386 trout into groups based on their species (all were in genus Salmo) and gender: ? ? Species Female Male Brown 68 56 Flathead 91 40 Ohrid 5 6 Sevan 61 59 A trout is to be selected at random. Given that the selected trout is male, what is the conditional probability that it is a Sevan trout?

Obesity is a growing public health concern worldwide. Adults with a body mass index (BMI) of 25 or greater are considered overweight or obese. The following table shows the number of adults (in millions) who are overweight or obese in countries with different income levels, based on data from the World Health Organization and the United Nations: ? ? Country income level Adults with high BMI (in millions) Adults with BMI < (in millions) Total High 549 414 963 Upper middle 612 1042 1654 Lower middle 288 1083 1371 Low 63 357 420 All 1512 2896 4408 What is the probability that an adult lives in a high-income country and has a high BMI?