By understanding probabilities, we can gain insight into how likely events are to occur. For instance, suppose that when a couple has a child, there is a 50 percent chance that the offspring is a boy. If the couple were to have two children, they would have a 25 percent chance of having two boys. We get this figure by multiplying the 50 percent chance of the first child being a boy by the 50 percent chance of the second child being a boy. In decimal form, this is 0.5 0.5 = 0.25 (0.25 is another way of writing 25 percent).
We can use probabilities in this way to help us identify who has the coronavirus. Here is how: First, consider the standard test. It takes a long time before this nasal swab test yields results and it is a hassle to get this test. I know people who recently waited three days for a test result. People believe getting tested is a hassle since it requires people to go to a designated place and sometimes it requires them to make reservations. As far as I can tell, it is unclear how accurate this test is, but let’s suppose that it is 95 percent accurate, meaning that it does not identify 5 percent of the people who have the virus.
Next, consider a different test that is only 90 percent accurate, so that it misses 10 percent of the people who have the virus. Suppose this test can be done at home by a patient – perhaps by using a test strip. Assume such a test is cheap and produces results quickly. Despite all of these advantages, a person may not be willing to use this relatively inaccurate test, especially, if the person is only faced with the choice of using the inaccurate test once and the accurate test once. So far, there are no surprises. We would all rather have a test that misses the virus 5 percent of the time rather than one that misses it 10 percent of the time.
However, we have another option, one that can allow us to use the cheap inaccurate test in such a way to produce more accurate results than the standard test provides. How? By using the cheaper test several times and relying on probabilities to convey information.
For example, suppose a person took the inexpensive test twice in a three-day period. If the results from the first test do not impact the results from the second test, we can use probabilities to learn if the person has the virus in much the same way that we used them to learn the likelihood that a couple would have two boys. We take the 10 percent error rate of the first test and multiple it by the 10 percent error rate in the second test to get 1 percent (This is 0.1 0.1 = 0.01 in decimal form). Think about this. The two inaccurate tests, when considered together, only miss identifying 1 percent of the cases. This result is much better than the one produced by the best test used just once, which in our example missed 5 percent of the virus’s cases.
Given the power of probabilities to convey information, the U.S.’s testing strategy should change to encourage people to use inexpensive tests frequently. Frequently used inexpensive tests will catch more people who are infected for two reasons. First, as we just discussed, the repeated tests on a person will be more likely to catch the virus than a single test would. Also, with inexpensive tests, people will be willing to test themselves at home when they would have been unwilling to go somewhere to get a test. As a result, more people will be tested, so more people with the virus will be identified. The implication is clear. Our government should adopt policies that encourage the development and distribution of cheap at-home coronavirus tests.