Question

the 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 n and v 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, \(n(N\cap V) = 171\) (number of vaccinated and negative), \(n(V)=1236\) (total number of vaccinated). So \(P(N|V)=\frac{171}{1236}\approx0.14\)

Step2: Calculate \(P(N)\)

The formula for probability is \(P(N)=\frac{n(N)}{n(S)}\). Here, \(n(N)=1171\) (total negative), \(n(S) = 2872\) (total number of people). So \(P(N)=\frac{1171}{2872}\approx0.41\)

Step3: Check independence

Two events \(N\) and \(V\) are independent if \(P(N|V)=P(N)\). Since \(0.14
eq0.41\), they are not independent.

Answer:

\(P(N|V)\approx0.14\), \(P(N)\approx0.41\), No