## Problem 3

Current testing standards for COVID-19 screening have the following characteristics, broadly speaking:

* The sensitivity of the test $P(+ \mid Infected)$ is 0.70.

* The specificity of the test $P(- \mid \mbox{Not Infected})$ is 0.95.

* Assume about 3% of the testing population is infected with the virus.

Hint: see the probability lecture overheads - sensitivity, specificity and prevalence were defined there. See the HIV blood testing example and video presentation of the HIV blood testing problem.

### Problem 3:Part A

What is the probability a randomly drawn person's sample tests negative for the virus?

Show relevant R computations in the following codeblock, show what you are computing, show how you obtain your answer.

```{r}

```

Answer:

### Problem 3:Part B

What is the probability a person has a covid infection given their sample tests negative for the virus?

Show relevant computations in the following codeblock:

```{r}

```

Answer:

### Problem 3:Part C

Consider $n=40$ people who are known to be infected by the virus.Suppose they are all tested and we observe $X=21$ of them test positive.Is the result $X=21$ unusual or surprising given the characteristics of the Covid-19 test?Explain your answer.Why or why not?Explain and show relevant computations used in the following code block.

```{r}

```

Answer: