Question

determining if two events are independent
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 independent. round your answers to the nearest hundredth.
$p(n|v)=\square$
$p(n)=\square$
are events n and v independent events? yes or no?\square

Explanation:

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

The formula for conditional probability is \( P(N|V)=\frac{\text{Number of people vaccinated and negative}}{\text{Number of people vaccinated}} \).
So, \( P(N|V)=\frac{771}{1236}\approx0.62 \)

Step2: Calculate \( P(N) \)

The formula for probability is \( P(N)=\frac{\text{Number of people negative}}{\text{Total number of people}} \).
So, \( P(N)=\frac{1371}{2321}\approx0.59 \)

Step3: Determine independence

Two events \( N \) and \( V \) are independent if \( P(N|V) = P(N) \). Since \( 0.62
eq0.59 \), the events are not independent.

Answer:

\( P(N|V) = 0.62 \)
\( P(N)=0.59 \)
No