statistics probability

Question

Suppose that the tourism board decides to look over their data on international tourists in the USA to make some predictions for when tourism resumes.

They find that the probability that an international tourist visits Austin given that they are a wine drinker is 0.6, and the probability that they visit Austin given that they are not a wine drinker is 0.4.

It is estimated that the probability of an international tourist being a wine drinker is 0.35.

What is the probability that an international tourist will visit Austin?

Answer 1

P(visiting Austin) = P(visiting Austin and not being a wine drinker) + P(visiting Austin and being a wine drinker) =

P(visiting Austin| being a wine drinker)P(being a wine drinker) + P(visiting Austin| not being a wine drinker)P(not being a wine drinker) =

.6(.35) + .4(1 - .35) =

.21 + .26 =

.47