the two - way table shows the results of a recent study on the effectiveness of the flu vaccine. let n be…

Explanation:

Step1: Calculate $P(N|V)$

The formula for conditional probability is $P(N|V)=\frac{P(N\cap V)}{P(V)}$. Since $P(N\cap V)=\frac{\text{Number of vaccinated and negative}}{\text{Total number of people}}$ and $P(V)=\frac{\text{Total number of vaccinated}}{\text{Total number of people}}$, then $P(N|V)=\frac{\text{Number of vaccinated and negative}}{\text{Total number of vaccinated}}$. From the table, the number of vaccinated and negative is 771 and the total number of vaccinated is 1236. So $P(N|V)=\frac{771}{1236}\approx 0.62$.

Step2: Calculate $P(N)$

$P(N)=\frac{\text{Total number of negative}}{\text{Total number of people}}$. From the table, the total number of negative is 1371 and the total number of people is 2321. So $P(N)=\frac{1371}{2321}\approx 0.59$.

Step3: Check for independence

Two events $N$ and $V$ are independent if $P(N|V) = P(N)$. Since $0.62\neq0.59$, the events are not independent.

Answer:

$P(N|V)\approx 0.62$ $P(N)\approx 0.59$ No