Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late).
Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar.
(a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3, and the two individuals #4 and #5.]
(b) Obtain cumulative distribution function of X, and use it to calculate P(2 ≤ X ≤ 6).