Exam 9: Independence and Conditional Probabilities

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among U.S. women ages 20 to 24 is 2791.5 per 100,000. Take a random sample of three U.S. women in this age group. What is the probability that all three women have a Chlamydia infection?

Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then which of the following probabilities is correct?

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 neither female nor hunt in medium-sized packs?

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among U.S. women ages 20 to 24 is 2791.5 per 100,000. Take a random sample of three U.S. women in this age group. What is the probability that none of the women has a Chlamydia infection?

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 male flathead trout?

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among U.S. women ages 20 to 24 is 2791.5 per 100,000. Take a random sample of three U.S. women in this age group. What is the probability that at least one of the women has a Chlamydia infection?

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?

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?

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 true positive happens when someone getting a mammography has cancer and receives a positive test result. What percent of women in their 50s taking a screening mammography receive a true 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: What percent of women in their 40s taking a screening mammography receive a positive test result?

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 both patients have high blood pressure?

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 neither of them has myopia?

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, given that the adult has a high BMI?

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 positive happens when someone getting a mammography does not have cancer and receives a positive test. What percent of women in their 40s 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 50s who takes a mammography to screen for breast cancer: The sensitivity of a screening test is the ability of the test to appropriately give a positive result when the person tested has a given disease. Which of the following is the correct notation for the sensitivity of a screening test?

Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, what may we conclude about the relationship between events A and B?

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. Jumping direction and jump outcome are independent.

Two-thirds of patients in a drug trial suffered from severe migraines as a side effect. Another side effect was impaired vision, with 25% of all patients having no impairment, 50% having some impairment, and 25% having severe impairment. Based on these probabilities, which of the following would be the correct tree diagram?