(a) What is the probability that all six are extroverts? Recall that the binomial distribution with parameters n, p, and r gives the probability distribution of the number of r successes in a sequence of n trials, each of which yields success with probability p. For this question, "success" can be defined as a professor being an extrovert. We are given that 45% of all university professors are extroverted. Therefore, each professor has a 45% chance of being extroverted. So, p = . Here we have six different professors; each one could be an extrovert or not. So, n = . To find the probability that all six professors are extroverts, we want six "successes." So, r =