Question 1: Intent – to – Quit Smoking. On December 2019, this study surveyed at random 1000 smokers about their intentions to quit smoking. The survey results showed that 25% of the surveyed smokers plan to quit smoking on January 1, 2020 (E1). As a follow-up, the same 1000 persons were surveyed on January 10, 2020 to see whether they did quit smoking. The follow-up survey showed that 30% of them actually quitted smoking (E2). Furthermore, the study showed that 80% of those smokers who planned to quit smoking actually quit smoking. E1 = Planned to quit smoking and E2 = Actually quit smoking
a) Find the probability that a randomly selected smoker planned to quit and actually quit smoking.
b) What is the probability that a selected smoker at random either planned to quit or actually quit smoking?
c) What is the probability that a randomly selected smoker planned to quit smoking, given that he or she actually quit smoking?
d) Calculate the probability that a randomly selected smoker is neither planned to quit nor actually quit smoking (Did not plan to quit and did not actually quit smoking).
e) Are the events E1 = Planned to quit smoking and E2 = Actually quit smoking independent, mutually exclusive or neither? Justify your answer.