Question

creating a two - way table from a scenario
in a study, 1,085 out of 2,371 people did not receive a flu
vaccination. 465 people were vaccinated and tested positive
for the flu. a total of 1,371 participants tested negative. create
a two - way table for the scenario.
465 791 1,236 425 800
1,085 956 1,371 2,371
use the two - way table to determine the probability of randomly
selecting a person who tested positive for the flu given he or she was
vaccinated

Explanation:

Step1: Determine the number of vaccinated people who tested positive

The total number of vaccinated people is \(1371\). The number of vaccinated people who tested negative is \(891\). So the number of vaccinated people who tested positive is \(1371 - 891=480\)

Step2: Use the formula for conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of a two - way table, if \(A\) is "tested positive" and \(B\) is "vaccinated", then \(P(\text{positive}|\text{vaccinated})=\frac{\text{Number of vaccinated and positive}}{\text{Total number of vaccinated}}\)

We know the number of vaccinated and positive is \(480\) and the total number of vaccinated is \(1371\)

Answer:

\(\frac{480}{1371}\)