Question

the two - way table shows the results of a recent study on the effectiveness of the flu vaccine. let n be the event that a person tested negative for the flu, and let v be the event that the person was vaccinated. answer the questions to determine if events n and v are independent. round your answers to the nearest hundredth. p(n|v) p(n) are events independent events? yes or no?

Explanation:

Step1: Calculate \(P(N|V)\)

The formula for conditional probability is \(P(N|V)=\frac{n(N\cap V)}{n(V)}\). Here, \(n(N\cap V) = 771\) (number of vaccinated and tested negative) and \(n(V)=1236\) (total number of vaccinated). So \(P(N|V)=\frac{771}{1236}\approx0.62\).

Step2: Calculate \(P(N)\)

The formula for probability is \(P(N)=\frac{n(N)}{n(S)}\). Here, \(n(N) = 1371\) (total number of tested negative) and \(n(S)=2321\) (total number of people). So \(P(N)=\frac{1371}{2321}\approx0.59\).

Step3: Check for independence

Two events \(A\) and \(B\) are independent if \(P(A|B)=P(A)\). Here \(P(N|V)\approx0.62\) and \(P(N)\approx0.59\). Since \(P(N|V)
eq P(N)\), the events are not independent.

Answer:

\(P(N|V) = 0.62\), \(P(N)=0.59\), Are events \(N\) and \(V\) independent events? No.