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 independent. round your answers to the nearest hundredth. p(n|v)=__ p(n)= are events n and v independent events? yes or no?__ pos. neg. total vaccinated 465 771 1236 not vaccinated 485 890 1375 total 950 1661 2611

Explanation:

Step1: Calculate $P(N|V)$

The formula for conditional - probability is $P(N|V)=\frac{P(N\cap V)}{P(V)}$. The number of people who are vaccinated and tested negative is $771$, and the number of vaccinated people is $1236$. So $P(N|V)=\frac{771}{1236}\approx0.62$.

Step2: Calculate $P(N)$

The number of people who tested negative is $1371$, and the total number of people is $2321$. 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:

$P(N|V)\approx0.62$
$P(N)\approx0.59$
No