4.66 Online Dating According to a BBC poll, nearly one-third of all Web users surf the Internet for a boyfriend or girlfriend. The BBC poll surveyed close to 11,000 Internet users in 19 countries. In Canada, according to another poll, only one-quarter of Internet users have tried online dating; 69% said that they would most likely not. Further, 64% of online daters say com- mon interests are the most important factor in finding a potential partner online, while 49% say physical char- acteristics (from photos and videos) are most important. Let A be the event an online dater will find a potential partner based on common interest. On the other hand, let B be the event an online dater will find a potential partner based on physical characteristics. An online dater is selected at random, and the following prob- abilities are given: P(AB) = 0.23, P(ANB) = 0.13, P(AB)=0.11, and P(A n B) = 0.53.

a. What is the probability the randomly selected online dater will find a partner based on common interests?

b. What is the probability the randomly selected online dater will find a partner on at least one of the two factors?

c. If the randomly selected online dater finds a partner based on common interests, what is the probability he or she will also find a partner with regards to physical characteristics?

d. Are the events A and B mutually exclusive? Explain.

e. Are the events A and B independent? Justify your answer.