Suppose that a marketing research firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with probability 0.40.
a. What is the probability that both questionnaires are returned?
b. What is the probability that neither of the questionnaires is returned?
c. Now, suppose that this marketing research firm sends questionnaires to ten different companies. Assuming that each company, independently of the others, returns its completed questionnaire with probability 0.40, how do your answers to parts a and b change?