1. A covid antigen rapid test has an accuracy rate of 65% (the probability the test show positive results when the patient has covid). The probability of having covid is 2% and the probability that the test is producing a positive result is 70%. What's the probability that a person taking the test and seeing a positive result has covid? (Show work)

There is a horrible disease spreading. If you get the disease, it will turn you into a shrubbery.

There are two different tests for the disease - one tests your blood and the other tests your saliva. The tests

are very rarely in error. You see on the news that the probability that a randomly selected person will test

positive for the first test is 0.2 and the probability that a randomly selected person will test positive for the

second test is also 0.2.

Your friend intends to have both tests done. Knowing that you are an expert in probability, he asks you:

"What is the probability that both tests will turn out positive?"

a. What would the correct answer be if the test results were independent?

b. Do you think that the two test results are actually independent? Explain.

c. Do you think that the right answer to your friend's question is higher or lower than what you guessed

in part a.? Explain in the context of part b.

Testing for Groate's Disease is very expensive, and positive tests are quite rare. To cut costs, a

hospital considers the following procedure: they pool blood samples from twenty patients (while preserving

the individual samples), and test the pooled blood. If the test on the pooled blood sample is negative, all 20

patients test negative. If the pooled test is positive, the samples are then tested individually to determine

where the positive blood came from. Suppose that the probability any one individual's blood is positive is. 018, and that the

samples are independent across patients.

a. What is the probability that a pool of 20 individual samples will test negative?

b. What is the probability that a pool of 20 individual samples will test positive?

c. Let N represent the number of tests required to determine positive/negative status of a group of 20

patients, when following the pooled sample procedure described above. What is the expected value of N?

d. Dr. House suggests that while the pooled procedure is superior to testing each sample individually, the

hospital can save even more money by pooling samples from X individuals, where X does not equal 20. Show that he is 6

correct.

Jorge, the famous Argentinian economist, builds a model/theory to only predict the probability that an individual has a significant other who is a male. He makes assumptions that imply this probability is a function of only the individual\'s hair colour and your body mass index. The exogenous variable(s) in his model are ____ and the endogenous variable(s) in his model are ____.

A) The individual's body mass index, hair colour, and gender | The probability of having a significant other who is male.

B) The probability of having a significant other who is male | The individual's body mass index and hair colour.

C) The individual's body mass index and hair colour | The probability of having a significant other who is male.

D) The probability of having a significant other who is male | The individual's body mass index, hair colour, and gender.