For each problem, write out the number of objects ($n$), the length of the sequence/sample ($l$), if repeats are allowed, and if you are computing permutations or combinations. 1 point for this on each problem
You do not need to use conditional probability to solve this problem
We are evaluating a new test to screen for Ebola that claims to identify Ebola in patients before symptoms are present . We want to use this test to quarantine probable cases to prevent the spread of Ebola. People can either not have Ebola or have Ebola and our test can be positive or negative. Let's take the random variable $E$ to indicate if the patient has Ebola and $T$ to indicate if the test is positive. We had 100 patients in our study who were at risk for Ebola. Our test indicated that 74 of the patients had Ebola and were quarantined to see if symptomps presented. After one week when symtpoms presented, we determined that 2 patients were not caught by the test and 6 of the quarantined patients presented with Ebola consistent with your test. The remianing patients did not have Ebola. Is catching 6/8, 75% of the patients with Ebola, indicate the test is effective? Answering this by completing the questions below.
[1 point] Write out the sample space
[1 point] What is the marginal probability of having Ebola?
[1 point] What is the marginal probability of having a positive test result?
[2 points] Compute $P(E = 1, T = 1)$
[3 points] What concept did we learn that could tell us whether or not the test is effective? How could we make a numeric argument?
[3 points] Is there compelling numerical evidence that the test is effective?