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 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:

Calculate conditional probability

Using the Conditional Probability Calculation and Two-Way Frequency Tables knowledge points

$$ P(N|V) = \frac{\text{Number of vaccinated people who tested negative}}{\text{Total number of vaccinated people}} = \frac{771}{1236} \approx 0.62 $$

Calculate marginal probability

Using the Two-Way Frequency Tables knowledge point

$$ P(N) = \frac{\text{Total number of people who tested negative}}{\text{Grand total}} = \frac{1371}{2321} \approx 0.59 $$

Determine independence

Using the Independent Events knowledge point

$$
LATEXBLOCK0
$$

Answer:

Answer the questions to determine if events N and V independent. Round your answers to the nearest hundredth.

\(P(N|V) =\) <blank>0.62</blank>

\(P(N) =\) <blank>0.59</blank>

Are events N and V independent events? Yes or no?
<blank>no</blank>