Please help,

Calculate the probability that:

Suppose that the test below has a $4\%$ false positive and a $7\%$ false negative rate. If the probability you

are positive $(+)$ is $2\mathrm{.}1\%,$ fill in the table and calculate the following: $($HINT: Values in the table are integers

or numbers with decimals,... NOT probabilities!!!$)$ This is important!

False positive: $0\mathrm{.}04$

False Negative: $0\mathrm{.}07$

Positive: $0\mathrm{.}021$

You

are

i$)$ Fill in the blanks above.

$(16$ pts$)$

ii$)$ The test below is accurate. $(2$ pts$)$

iii$)$ The probability that a positive test means you have the disease. $(2$ pts$)$

iv$)$ The probability that a negative result means you are negative. $(2$ pts$)$

v$)$ John Oliver was outraged that a test can be wrong $50\%$ of the time when it comes back

positive. If a standard medical screening test is as accurate as what you just calculated,

does that make the test inherently bad? $(2-3$ sentences$)(3$ pts$)$

vi$)$ Since the positivity rate for COVID$-19$ tests are about $3\%,$ do you think it is fair to tell

everyone that tests positive with this screening test they are not allowed to work for $2$

weeks and they will not get paid for their time off? $(2-3$ sentences$)(3$ pts$)$