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.

A 4-column table has 3 rows. The first column has entries Vaccinated, not vaccinated, total. The second column is labeled Positive with entries 465, 485, 950. The third column is labeled Negative with entries 771, 600, 1,371. The fourth column is labeled Total with entries 1,236, 1,085, 2,321.

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?

Answer 1

P(N|V) = 771/1236 ≈ 0.62

P(N) = 1371/2321 ≈ 0.59

Are N and V independent? No — because P(N|V) (≈0.62) is not equal to P(N) (≈0.59).