Internet retailers have so much data!Epods.com finds that there is a 10% chance that a visitor buys a product.Using sales data over the past two years, you've helped them realize that if a visitor spends a long amount of time on the site (i.e., more than 5 minutes), it effects the probability of the visitor buying a product.In particular, among all the buys made by visitors, 80% of time the visitor spent a large amount of time on the site.Among all the visits that resulted in no buy or purchase, 25% of the time the visitor spent a large amount of time on the site.

1)[10 pts] What is the prior probability of a visitor buying a product?

2)[10 pts] What is the conditional probability of a visitor spending a long amount of time on the site, given that the visitor makes a purchase?

3)[10 pts] What is the conditional probability that a visitor buys a product given that the visitor spends a long amount of time on the site?

4)[10 pts] What is the conditional probability that a visitor does not make a purchase given that the visitor has spent a long time on the site?

5)[10 pts] What is the conditional probability that a visitor makes a purchase given that the visitor does not spend a long time on the site?