Final answer:
The random variable X represents the number of adults surveyed until finding one who will watch the Super Bowl. It can take on values of any positive integer and follows a geometric distribution with a probability of success of 40%.
Step-by-step explanation:
The given scenario is a probability problem involving a geometric distribution, which is related to the number of trials needed to get the first success in a sequence of independent Bernoulli trials.
Define Random Variable X
a. The random variable X is defined as the number of adults we must survey until we find one who will watch the Super Bowl. Here, 'watching the Super Bowl' is considered a 'success'.
Values of X
b. The values that X can take on are all positive integers starting from 1, as we must survey at least one person and there is no upper limit to the number of people we might have to survey before we find a 'success'.
Distribution of X
c. The distribution of X is a geometric distribution. Since the probability that an adult will watch the Super Bowl is 40%, the probability mass function (pmf) of X is: P(X = x) = 0.6(x-1) * 0.4 for x=1, 2, 3, ... This is denoted as X~Geom(0.4).