1. The probability that a person fails to meet CDC Physical Activity Guidelines for both aerobic and muscle-strengthening activity is 0.77. The probability that a person eats a poor diet based on the American Heart Association's healthy diet score is .48. The probability that a person fails to meet the Physical Activity Guidelines and eats a poor diet is .42.

a. What is the probability that a randomly selected person fails to meet the activity guidelines or eats a poor diet?

b. Find the probability that a randomly selected person is leading a healthy lifestyle. That is, they meet the Physical Activity Guidelines and eat a diet that is not poor. Include a Venn diagram in your response.

c. If you randomly select 4 people, what is the probability that they all eat a poor diet assuming independence?

d. If you randomly select 3 people, what is the probability that the first one meets the Physical Activity Guidelines and the last two do not?

e. Compute the probability a person fails to meet the Physical Activity Guidelines given that they eat a poor diet. Compare this to the probability a person eats a poor diet given that they fail to meet the Physical Activity Guidelines. Are they the same?

2. It is estimated that approximately 12% of the population has a certain disease. The standard test for the presence of the disease is good, but not 100% accurate. If the person has the disease, the test will return a positive result with a probability of .92 (sensitivity). If the person does not have the

disease, the test will return a negative result with a probability of .985 (specificity). A randomly selected person is tested for the disease.

a. Draw a probability tree describing this situation.

b. Compute the probability the randomly selected person will receive a positive test result.

c. Given the person receives a positive test result, compute the probability they have the disease. This is called the positive predictive value.