Question

A researcher surveyed people as they left a museum, asking whether they visited the gift shop and whether they watched the film about the museum's history. The table shows the relative frequencies of the responses. One person who was surveyed is randomly selected.
What is the probability that the person visited the gift shop, given that the person did not watch the film?
Write the probability as a percent. Round to the nearest tenth if needed. Show all of your work for credit!

Answer 1

Let event G represent that a person visited the gift shop and event F represent that a person watched the film.
P(G) = 0.46
P(F) = 0.49
P(G') = 0.54
P(F') = 0.51
P(G and F') = 0.1
The probability that the person visited the gift shop, given that the person did not watch the film
= probability that the person visited the gift shop and did not watch the film divided by the probability that the person did not watch the film
= P(G and F') / P(F')
= 0.1 / 0.51 = 0.196 = 19.6%