Question

The Franklin County health department is investigating vaccination rates and effectiveness for the HPV vaccine among college students. 424 college students from area colleges were studies. Vaccination status and infection status was obtained by medical record. Results are shown in the table below:

Active Infection	Recovered Infection	Not Infected
Vaccinated	22	30	176
Not Vaccinated	46	48	102

Suppose a randomly selected student is not infected. What is the probability that this student has been vaccinated?Calculate the probability that a randomly selected college student from Franklin County has been vaccinated.

Calculate the probability that a student who has not been vaccinated has either an active infection or a recovered infection.

Calculate the probability that a randomly selected college student from Franklin County has an active infection.

The health commissioner is interested in reducing the rates of active infection. Describe what would happen to the probability of active infection if vaccination rates increased in Franklin County. Provide specific numbers or calculations from the question to support your answer.

Answer 1

	Active infection	recovered infection	not infected	total
vaccinated	22	30	176	228
not vaccinated	46	48	102	196
total	68	78	278	424

A)
P(V | NI) = P(V and NI)/P(NI) = 176/278 = 0.6331

B)
P(vaccinated) = 228/278 = 0.8201

C)
P(AI or RI | NV) = (48 + 102)/196 = 0.7653

D)
Active infection in case of vaccination is very low.
hence increasing the vaccination reduces the active infection